I have read that "every positive number $a$ has two square roots, positive and negative". For that reason I have always (as far as I could remember) unconsciously done the following for such expressions
$$ x^2 = 4 \implies x= \pm 2 $$
What I wanted to know was that, in order to cancel the square, aren't we taking square root on both sides? If we are, why don't we have something like this: $$ x^2 = 4 $$ $$ \sqrt{x^2} = \sqrt4 $$ $$ \pm x = \pm 2$$
Why do we always end up with this instead $$ x = ± 2\quad ?$$