Solutions of $\sqrt{x^2+5x-14} + |x^2+4x-12|=0$ My attempt:
Given,
$$\sqrt{x^2+5x-14} + |x^2+4x-12|=0 \tag{1}$$
Since $|a|=\sqrt{a^2}$, $$\sqrt{x^2+5x-14}=-\sqrt{(x^2+4x-12)^2}$$
Squaring both sides, $$x^2+5x-14=(x^2+4x-12)^2$$
When I simplify the above, I get two real solutions: $x=2$ and $x=2.138 \text{ (approximately)}$. However, there is only one solution to equation $(1)$ according to Wolfram Alpha, $x=2$.
Is my solution incorrect? If so, where did I go wrong?

When you square, you may get additional solutions. You need to test those solutions in the original equation.
Alternatively,
$\sqrt{x^2+5x-14} + |x^2+4x-12|=0$
$\implies x^2+5x-14 = 0 \ \text { and } x^2+4x-12 = 0$
$\implies (x-2) (x+7) = 0 \ \text { and } (x-2)(x+6) = 0$
So only solution that works is $x = 2$.
