# Step-by-Step Math

*(January 15, 2014 Update: Step-by-step solutions has been updated! Learn more.)*

Have you ever given up working on a math problem because you couldn’t figure out the next step? Wolfram|Alpha can guide you step by step through the process of solving many mathematical problems, from solving a simple quadratic equation to taking the integral of a complex function.

When trying to find the roots of 3*x*^{2}+*x*–7=4*x*, Wolfram|Alpha can break down the steps for you if you click the “Show steps” button in the Result pod.

As you can see, Wolfram|Alpha can find the roots of quadratic equations. Wolfram|Alpha shows how to solve this equation by completing the square and then solving for *x*. Of course, there are other ways to solve this problem!

Wolfram|Alpha can demonstrate step-by-step solutions over a wide range of problems. This functionality will be expanded to include steps for solutions in other mathematical areas. Look through the following examples to see the abilities of the “Show steps” functionality.

If you need to learn how to do long division of polynomials, Wolfram|Alpha can show you the steps. Let’s try (*x*^{5}–14*x*^{4}+3*x*^{2}–2*x*+17)/(2*x*^{2}–*x*+1):

If you are stumped trying to find the limit of *x ^{x}* as

*x*->0, consult Wolfram|Alpha:

When you need to find the derivative of (3*x*^{2}+1)/(6*x*^{3}+4*x*) for your calculus class, Wolfram|Alpha will find this derivative using the quotient rule.

Are you trying to integrate *e*^{2} *x* cos(3*x*), but forgot the formula for integration by parts? Wolfram|Alpha will remind you how to integrate by parts.

Wolfram|Alpha can do virtually any integral that can be done by hand. Try the integral of *x*?[1–?[*x*]]:

Wolfram|Alpha also has the step-by-step functionality for partial fractions. Try partial fractions of 1/(*x*^{3}–1):

The step-by-step programs in Wolfram|Alpha rely on a combination of basic algorithms and heuristics including Gaussian elimination, l’Hôpital’s rule, and Bernoulli’s algorithm for rational integration. These heuristics are a logical formulation of the natural methods used by humans for solving problems. By utilizing *Mathematica*’s powerful pattern-matching capabilities, Wolfram|Alpha’s developers have morphed these rules into a platform for breaking down and structuring the solutions to complicated problems, which closely mimics the ways by which a human would solve problems of these natures.

The “Show steps” feature allows you to learn basic mathematics on your own, or it can simply be a nice way to check your work! It can also give you insight on different ways to solve problems. So next time you find yourself ready to give up on a math problem, make sure to check with Wolfram|Alpha. Visit the Wolfram|Alpha Homework Day Gallery for examples of how you can use Wolfram|Alpha as a learning tool for other subjects.

Am I the only one to have noticed that the steps text is incorrect.

In text it say subtract 7/3 sides when in the equation its add 7/3 to both sides.

It says subtract -7/3, which is the same as adding 7/3.

No, it’s just clunky. It says subtract -7/3 i.e. add 7/3.

Thankyou for pointing out how the ‘Show Steps’ function is triggered. I had heard of it but never met it in use. There are many such links on the answers which are easily overlooked.

I would like to know how to plot a grayscale with Wolfram Alpha. I apologize if this comment is off site.

You should be able to use the ContourPlot function from mathmatica int W|A:

http://reference.wolfram.com/mathematica/ref/ContourPlot.html

Miguel, i’d like also to know it. Sorry for offtop, nut explain us please ;)

This is awesome!!!, but was it really worth the work :/ ???

This is pretty nice… I would like to see the interface enhanced so I could enter several math problems at once (for example: Chapter 7, problems 1-19 (odd)) and have the output in a printable / customizable format (ie a script font that looks like my handwriting).

But, this is definitely a great start! Thanks :)

That would be really sweet, but that would require going through all the textbooks in all the high schools of the country and it recognizing where you are to base your school district and analyzing the textbook that that district uses.

In other words, it’s impossible.

Love the idea though.

How many people thought Wolfram Alpha would be possible 10 years ago…

Wonderful, this looks fantastic, great work. I can’t belief it!

I use W|A with my Grade 9 students as we solve linear equations and go over the Show Steps button. They were amused because it is inefficient: it equates to zero first and then isolates the variable. (Please keep it that way…)

I wish this had existed when I was still in school. Easily one of the most exciting things I have seen recently.

When are we going to be able to define some variables of a function as constants and not variables??! This is tremendously limiting.

congratulations on killing textbooks, wolfram. I’m sure scores of old people will be telling kids about their hey-day now.

wow now it is going to help me a lot… because I am very poor in maths.

Thanks

I shall be thankful if you please help me in solving a problem

show that

3^2008 + 4 ^2009 can be written as product of two +ve integers each of which is larger than 2009 ^182

This is mostly curiosity, but why is there now a post about this feature? Hasn’t it been implemented since wolfram alpha first started?

Or has there been a major overhaul that shows full working/solutions for more types of equations? The equations I tend to use it for, usually says (step-by-step results unavailable’

anyway this feature is awesome, and I use it quite a lot to aid my learning.

Awesome! I wish I had this feature few years ago while studying at University.

I was solving a lot of math helping other students and raising my wellfare, and this feature would be dramatically useful.

They are all easy except the partial fraction which is kind of different. Not hard but different lol lol

The log to the base a of b is the same as

log(a)/log(b)

Hi

To obtain the logarithm with a fraction as base you have to write the base without the 0 before the decimal point:

Log .5 of (x^2+2x)

To obtain a logarithm in base 1/2

Hope it helps, it sure took me a while :)

Greets and thanks to the people behind WA!

Better yet, use the Wolfram Mathematica notation:

Log[base,ecuation]

ex: log[1/2,x^2+x]

it is always a good ide to look for the mathematica syntax

If you try to solve a limit, but the left-handed limit and the right-handed limit are not the same, Wolfram Alpha gives both one-sided limits, but the “show steps” button doesn’t appear. Is there a way to make it come up? Or to request only one of the one-sided limits and have the button appear?

f(x) = x^2 – x + 1, f((2+h) – f(2))/h.

How could I input this equation to get a step by step process to solve this difference quotient?

Tried it. But wolfram simply spit back the equation back at me, not the solution.

WS

a good site but it must also open for other branch of math

this is totally fantastic and very useful to all students.. this is the very beginning of great change in terms of search engine ..

very beautiful site it is awesome it is a good tool for all students .it will be very nice if they can include more fields of mathematics.

The “show steps” botton does not show in any of the problems I had to do :( I’m sad.

The computations this can do are very impressive, especially with integration.

However, i wish there was a way to modify the input to perform integrals according to specific methods i.e. simpson’s rule, partial fractions, ect.

Does anyone know if this as the ability, or does it have to be done specifically in a notebook?

That’d be really useful!!! I think it’d be really cool if we could save problems that we’ve done, if need be. (There are times when I have to re-type my question because I’ve moved on and then decided to take another look at it.) Also, I wish W/A could compute answer for the Trapezoidal Rule without a condition. (None of my math problems for Trapezoidal Rule ever have conditions. They only ever give me the equation and say “with n = 8”.

This is very beautiful site for the children and it will help lot more to others who are not understand the maths properly.

Can you solve this;

Ten not necessarily distinct positive integers have the property that if all but one are added, the positive results are 82, 83, 84, 85, 87, 89, 90, and 92.

I need some help with this.

David

I notice that maths solving problem is not correct. If any one can solve this properly.

Guys is incredible what you has achieved lately!

btw the link of the limit x^x example is wrong:

http://www.wolframalpha.com/input/?i=limit+of+xx+as+x-%3E0

it should be:

http://www.wolframalpha.com/input/?i=limit+of+x^x+as+x-%3E0

Math is not for for me but still i have to study it :( :D great work though

It is not showing steps for negative exponents.

like: (2x^0Y^2)^-3 * 2yx^3 Wow thanks for the answer but how did you do it?

It is not showing steps for negative exponents.

like: (2x^0Y^2)^-3 * 2yx^3 Wow thanks for the answer but how did you do it?

Can you enter negative exponents?? Have not been able to do it.

What a informative post Step-by-Step Math in wolfram alpha blog. Really problems steps discussed in detail manner. I like this. I show this post to everyone in my family. Really i enjoyed most. Thanks for sharing a very informative blog.

Wow, I’ve got to get deeper with my maths skills. It looks neat but I got lost pretty quickly:)).

What an amazing search engine. I don’t know what to say thay you guys at Wolfram|Alpha really did a greeeeeaaat job making this such amazing engine into operation. I just wonder how math student use this engine on their exams. Should they solve the equation manually, or just put it inti Wolfram|Alpha?

WOW. I have never seen anything quite like it before. Solving maths problems in a search engine that even show steps and people thought google was the best, not anymore. I tried tanx/x without limits and as x approaches 0 and result BING. I am just so impressed, mathematics happen to be my favorite subject and i think i am going to spend my free time here. Next i tried TNT, it gives options as a finance entity, chemical compound so i choose chemical compound and i get the forumula, structure, IUPAC name and properties. This will take education to a new level.

Just want to ask are those values fed in database or calculated in real time and then cached.

Will be back soon.

its very interesting very helpful site 2 those who r really interested in math

so, i used wolfram to find x in 4^x-3^(2x)=6 but i cant seem to find the steps. any help?

this is totally fantastic and very useful to all students.. this is the very beginning of great change in terms of search engine ..

What a informative post Step-by-Step Math in wolfram alpha blog. Really problems steps discussed in detail manner. I like this. I show this post to everyone in my family. Really i enjoyed most. Thanks for sharing a very informative blog…thanks a lot………….

Hey

Doing some math and using Alpha to check my answers, its fine when they are correct but when they aren’t I cant check the correct calculations like you show here in this step by step post. I have no show/hide steps button. Any suggestions?

Hi Andre, Can you provide us with a few of the inputs that you tried? We’re happy to take a look.

Hi, I have a similar problem with one limit:

http://www.wolframalpha.com/input/?i=lim_%28x-%3E0%29%28sin%28x%29%2Fx%29%5E%281%2Fx%5E2%29

The answer is correct but when I want to see steps it says “step by step result unavailable”.

pretty much any derivative i try to calculate it gives me the answer but i cant see the steps. for example, derivative of ((sin x)^-5)-((cos x)^3). i used wolfram alpha to solve this and many other problems a few days ago and it showed the steps just fine but now it won’t. wondering what’s going on thanks

If only, i came across this article during my school days……..thankfully, i am off maths. anyway great post for all the folks that are struggling with maths.

i just tried doing the derivative shown as an example in this post and and not even that one would allow me to see the steps. very frustrating!

Hi Ally,

Can you give us the an input that you tried. We will check it out. Thank you.

The show steps isn’t working for any derivatives I’ve been trying. :(

Hi Steve, We’re happy to look into this. Can you give us the input that you tried? Thank you.

By the name of Allah the most merciful and the most gracious

the wolframeAlfra site is fantastic and very good website

I will tell all my friends about it

Thanks for this good work

When I enter y”+4y=(x^2-3)sin(2x), I cannot see the steps. this would be helpful because I also did it by hand and I got a different answer (the one given from Wolfram is correct). It would be amazing to figure out where I made my mistake

No matter what function I put in, it seems as though the show steps part of the derivative doesn’t work. I click show steps and it looks the same as it was before.

Yeah, the show steps for derivatives does not seem to be working. At least it isn’t working for me.

I have been using the “show steps” and it was working perfectly until a few days ago. I too have been trying to take derivatives and the answers are correct, but it will not display the steps (I also have the iPod app and the same problem is happening there. An example I’ve tried is: y = (x-3)/(4x+2)

I haven’t been able to get any of the “show steps” to work for derivatives. I have tried using different browsers (Chrome, Firefox, and IE7) tried adding and removing add blocking software. Nothing seems to have any effect whatsoever, when you click “show steps” the web page loads like it’s attempting to show the normal step-by-step but doesn’t ever display anything, even though the button does change to “hide steps” no other changes are visible. Please fix this website, to me this is the alpha and the omega (pun intended), and I can’t wait to have full functionality back!

Hi all, Thank you for bringing this to our attention! Our team is working to get this back up and running. Thank you.

I have also purchased the Wolfram Alpha mobile application (Android OS) and this same show steps functionality is as it is on the rest of the site, not working.

It would be awesome to have the steps on

FullSimplify[(2 - Sqrt[2 + Sqrt[3]])/Sqrt[2 - Sqrt[3]]]

(I am using a slow connection. I heard this might be the problem?)

If my radius=1 ,what would be the height of the line from the tangent point if it covers 25 percent of the circle area.

Although I see that for some maths the site is now showing the steps again I cannot get the show steps for 2nd order ODE’s such as:

2y” +y’ +3y = x^2 +6

What would I need to type in to get the steps, or do they simply not show for this type of maths, or is the maths still not 100% working!

Whenever I input a problem with i (the imaginary number, sq.root of negative one) it doesn’t show the solve button :s

whenever i type in an equation ill either get a “result” (which im assuming is the answer) or i just get nothing at all (which is most of the time) how come im not getting any answers?

Hi Amanda,

Can you provide us with a few of the inputs that you tried? We’re happy to take a look. Thank you!

I just wanted to say, i’ve been with Wolfram alpha since the day it went public back in may 2009, and i have to say this site has helped me more though my advanced math classes than any calculator, textbook or teacher ever could. thanks for making this site what it is!.

When I enter integrate (3^x)/(4-9^x)dx, I cannot see the steps. this would be helpful because I also did it by hand and I got a different answer (the one given from Wolfram is correct). It would be amazing to figure out where I made my mistake

Hello Serg, Wolfram|Alpha doesn’t show steps for every function yet. We are continually working to support more step-by-step functionality. Thank you!

http://www.wolframalpha.com/input/?i=integrate+(3^x)/(4-9^x)dx

Hello Zac, What are you experiencing when you enter this input? This input is working okay here:

http://www.wolframalpha.com/input/?i=factor+500a^3%2B32

Jumping on the bandwagon here: the show steps feature doesn’t seem to be operational for this problem:

integral of (cos(n * cos^-1(x))) from -1 to 1

Hi, i have done 20 diferent questions online and NONE have come up with a more steps option. Example : y-2=((-5-2)/(-3+1))(x+1)

Hello Matt,

We don’t support step-by-step for LaPlace Transforms yet either… we will in the future.

Thanks!

When will step-by-step support for LaPlace transforms be implemented (at least providing table used)?

I cant seem to get steps for

integrate (1/(x(pi-2*x))) [(pi/6),(pi/3)]

Hello Tharkaan,

Our developers are continually adding step-by-step support for math problems. At this time, this specific integral is not yet supported.

I can’t get steps to show for anything. I even tried using the identical limit example pictured above and the steps don’t show for me.

Hi abney317,

Thank you for bringing this to our attention. Would you mind telling us what browser/operating system you are on?

Thank you,

Wolfram|Alpha Team

Oddly enough it works fine at my home computer.

At school I was running FF 3.6 on Win7… didn’t work on IE 8 either…

at home I’ve got FF 4 on Win7 and it’s working perfectly

Hi,

I need to solve summation problems. but I cannot get step by step solution for summation problems. do you provide step by step solution for summation problem or not???

http://www.wolframalpha.com/input/?i=integrate+1%2F%28x^2%2B4*x%2B5%29+from+x%3D-2+to+-1

steps do not work

Hello Tana,

We don’t support step-by-step for this yet… we are constantly adding new step by step functions everyday. Stay Tuned!

Thanks!

I’ll pay for the program that shows step by step on a consistent manner. Wolfram Alpha is fantastic and don’t get me wrong Mathematica is also amazing, but I can’t believe this key area for students hasn’t been more developed. It would be a sellout instantly. Please help! Thanks.

Then check Mathway.

Sadly it’s not free. :(

Anyway, I tried some inequalities and the examples pictured in the above blog post, but step by step didn’t show up.

I’m on chrome (win7).

Is there somewhere where we can check what functions have full or partial “step-by-step” functionality? Would be great to have.

And is there any step-by-step functionality in the algebra section? I’d really like to show WA to my students, but the course is for algebra, and it’s not very good if they can only get the answers without the full explanation.

dane jest równanie okregu x2+y2-2x-3=0

zapisz równanie tego okregu w postaci kanonicznej i wypisz wspó??edne oraz promie? okr?gu

A C.N.A. offeres a patient 10 ounces of water. The patient drinks 180 milliliters of water. How much is left?

when i try to work out the simultaneous equation y=2x-7 and x^2+y^2=61 it wont show steps is this because it works it out using a graph if not then how can i see the steps?

hi..I would step by step in operation with matrix, lowreduce, solve ecc ecc..is possible? thk!!

Hi

I haven’t been able to get any of the “show steps” to work for definite integrate.

I just want to know if you don’t support step-by-step for this yet.

Thanks

As far as i’ve seen you can only show steps for functions, etc.

Why is there no ‘show steps’ button for normal calculations (not involving variables) such as

4 / 2^(3/2) ? For lower-level mathematicians like me, who don’t understand the steps going from 4 / 2^(3/2) to sqrt(2) this is very difficult to find out.

[...] show one way of reaching the solution with the “Show Steps” button. Check out the post “Step-by-Step Math” for more on this [...]

[...] in a wide variety of areas, including finance, nutrition, chemistry, astronomy, math, travel, and even solving crossword [...]

i want to calculate complex varible. step by step. so that program don’t show step on

I tried putting in an equation, and the answer came up fine, but no show steps button is to be found :/

please I need a step by step answer to my question,, My question is:

16 ounces of fresh juice contains 216 calories and 16 ounces of grapefruit juice contains 174 calories. If 8 ounce mixture of these 2 juices contains 94 calories then what fraction of the mixture is the orange juice?

Please answer this question to my email as early as possible,,

my Email ID is ahmadbsseimportant@yahoo.com

I am looking for some more basic algebra skills etc for Middle school math. I am not finding step by step math for this age group. Please advise… Is there a place I can find it? Or a way to add some examples?

Wolfram|Alpha Mathematica used to be the source I would go to in order to check my work and answers. Unfortunately, now that I need it again for my Calculus 3 course, the answer will come up, however the “step-by-step” option is no longer there. The most important part is making sure I know how to do the problems correctly, not just the answer. Has this option permanently been discontinued? If not, when will it be back?

Find a factor (divisor) of

12702047 other than 1 & itself

Hey Wolfram ALpha – I have here a simple sqrt and I want to know the solution to this:

((2*sqrt(3))/sqrt(2))^3 – it shows me the solution but I dont know how you solved this.

How do I input a table of paired values to get a fitted curve?

There are some diiferential equations for which wolfram alpha doesn’t give me the show steps options. Why is that. The equation i put in was this; y”[x] + 3*y’[x]*y[x] + (y[x])^3 = 0. And this y”[x] + x/2 y[x] = 0. The second one I can understand as it’s a special function but it should give the option for the first one at least.

Putting in -x = -8 won’t give me a show steps button. Neither will 2/9 + x = 1/3.

There are some expressions where it is not useful as it is supposed to be. For example with (d/dx a^x) it doesn’t show useful steps. For example, it could show the chain rule method.

Where do I find the “show steps” button?… It is not in the same place as on the illustrations

write the equation of the lie satisfying the givenn conditios. Label two points o the line.

parallel to y=4x+1 and passing through the point (0,-3)

Limit of {(2x-3)(sqrt x-1)}/(2x^2+x-3) as x approaches 1

please solve this and mail the solution to gbaidco@gmail.com.

[...] Step-by-step math. [...]

How do I print the step by step results? I get nothing in my print preview.

please show me solving step by step sum(1/j^2)j=1..infinity

when i enter:

solve x=sqrt(2)*sqrt((6-x)/x)

it gives me the solution but when i click on show steps, it tells me they are unavailable

pls i need to solv this

1000000=x-(10%of x),what is x?

Your program shows the answer to sum_(k=1)^(2000)2/(4^(k/2001)+2) but it doesn’t show how it has reached the answer.

can you show step by step input to solve this integral using wolfram mathematica software?

integrate sin^n xdx for n = 1, 2, 3, . . . , 10.

plz anyone with correct answers answer these with step by step easy please:)

3x-3=-2x+2

andd :

how do I use wolfram alpha if i want to find the second derivative ?

Hello

Why does W|A answer “Step-by-step results unavailable” when I ask for the limit of sin(x) / x as x -> infinity ?

Thx

This is a great tool to use when in need of math help :)

in simple example like 2/9 + x = 1/3 or 3x^2+x–7=4x, some step unnecessary. but this is great tool, it’s free, amazing…

the function would be great — but I’ve found that in questions where there are separate tabs for “result” and other representations( i.e. derivative or indefinite) … the “show steps” only works for the representations. Neither of those alternate representations help me comprehend or answer the problem.

it should also be noted that “verification” — the process of showing two equations are equal to one another — simply states whether it is true or false, I have not seen an option to show the steps for the process it used.

y + (1/x) = 7/2,x + (1/y) = 7/3

NOR

partial fractions of [y + (1/x) = 7/2,x + (1/y) = 7/3]

Does not show steps

PV=FV/(1 + i) N

PV=850/ (1+0.12)10

=850/3.10585 ( This is the step I do not understand how did we get 3.10585)?

=273.68

how to do ath- patterns and functions?? beg you please help me

Excellent explanation and information on solving the problem.

It’s really nice Post, I like the way of presentation..

thanks for such nice Post..

I would like to know how to plot a grayscale with Wolfram Alpha. I apologize if this comment is off site.

Hello Serg, Wolfram|Alpha doesn’t show steps for every function yet. We are continually working to support more step-by-step functionality. Thank you!

Too bad that Wolfram Alpha doesn’t allow the step-by-step solutions for inverse of functions…:(

Really nice blog this will definetely going to help my kids to study extra. Thank you

useful mathematical Step-by-step solutions. good stuff…..