SOLUTION: Explain the error made in solving the equation. Solve the equation correctly x^2=x x^2/x=x/x x=1 I thought the error was that x^2 is not equal to x, but rather x^2 is equal

Question 395137: Explain the error made in solving the equation. Solve the equation correctly
x^2=x
x^2/x=x/x
x=1
I thought the error was that x^2 is not equal to x, but rather x^2 is equal to x*x and so it should have been multiplication and not division-yet I really don't know I am only taking a guess. I also don't know how to go about solving the equation itself
Found 3 solutions by stanbon, Earlsdon, richard1234:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Explain the error made in solving the equation. Solve the equation correctly
x^2=x
x^2/x=x/x
x=1
I thought the error was that x^2 is not equal to x, but rather x^2 is equal to x*x and so it should have been multiplication and not division-yet I really don't know I am only taking a guess. I also don't know how to go about solving the equation itself
====================
So, what is the solution ?
x^2 = x
x^2-x = 0
x(x-1) = 0
x = 1 or x = 0
----
The method used in the problem found the x=1 solution but not the x=0
solution.
---
Of course you could't divide both sides by x if x = 0.
But you did. And that is the mistake.
----
Cheers,
Stan H.
Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Your solution is good!
Remember that there is only one number whose square equals the number itself, and that is 1 since:
so the solution to:

Divide both sides by x.
leaving you with:

Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
The process is correct. However you're assuming that , since you're dividing by x (this part is the mistake) which is assumed to be non-zero so that the operation is defined. If x = 0, the equation is still true, so x = 0 or x = 1.

The best way to solve this is to move x to the other side to produce

x = 0, 1

Or, you could do it like the way you did in the question (assuming ), then do the case and see if it works. However the first method is more solid.
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