Solve for x. x^2 - 2x = 0
The Attempt at a Solution
If I solve this equation by factoring out the x first, as in x(x-2) = 0, I get that x = 2 or x =0
However, if I add 2x, as in x^2 = 2x, then I divide by x, leaving x = 2
My second method only has one answer. What happened to x = 0?
When I solve equations like this, what should I do to guarantee that I get all of the solutions without using a graphing calculator?