Note: sqrt = square root of
sqrt(x^2 - x) = 2*sqrt(x - x)
If you start by squaring both sides you get:
x^2 - x = 2^2 * (x - x)
x^2 - x = 4(x - x) But x - x = 0, So the right hand side of the equation is zero. You could have deduced this from the beginning, but the hint instructed that you start by squaring both sides, so I figured it would be better to follow those instructions.
So, we have x^2 - x = 0.
Factor out an x to get:
x(x-1) = 0.
The solutions are x = 0,1. I am extremely sorry for not noticing my mistake earlier.