Question

How do you solve using the completing the square method `x^2=x`?

Answer 1

This would be a very roundabout way in this case.

Explanation:

`->x^2-x=0->x(x-1)=0->x=0orx=1`

Completing the square (if you really must):
`x^2-x=0`, so the number with `x` is `-1`
Take half of that and square it:
`x^2+2*(-1/2)*x+(-1/2)^2=(x-1/2)^2`, is the square we look for.

We have to add the `(-1/2)^2` also to other side.

So: `(x-1/2)^2=(-1/2)^2`

`->x-1/2=+-1/2->x=0orx=1`

I prefer the first way, to be honest, but if you have to use the other method, you can still use the first to check your answer.