Question 189450
{{{x^2 = x}}} While canceling (dividing by) an x on both sides seems to be a valid mathematical operation, it ignores the fact that the equation is, in fact, a quadratic equation and will have two solutions (roots or zeros).
The correct procedure is to subtract x from both sides giving you...
{{{x^2 - x = 0}}} The factor an x from the left side:
{{{x*(x-1) = 0}}} Now apply the zero product rule:
{{{ x = 0 }}} or {{{x-1 = 0}}} so the two solutions are:
{{{ x = 0 }}} and {{{x = 1}}}