Question

$|x|^{2} + |x| - 6 = 0$

Answer 1

The solutions to the equation are $x = 2$ and $x = -2$.

Answer 2

Let $y = |x|$. The equation becomes $y^2 + y - 6 = 0$. Factoring gives $(y+3)(y-2) = 0$, so $y = -3$ or $y = 2$. Since $y = |x| \ge 0$, we must have $y = 2$. Thus, $|x| = 2$, which means $x = 2$ or $x = -2$.