I have to solve $x^2 + 4x + 4 = 7|x+2|$.
I did this: $(x + 2)^2 = 7|x+2|$
And we know that $|w| = w \iff w ≥ 0$, so:
$|x+2|^2 = 7|x+2|$ because the $(x+2)^2$ is always $≥0$
Then, I divided this equation by $|x+2|$ (I think I can, because the $|x+2|^2 = |x+2||x+2|$
so I got $|x+2|=7$
It means that $x = 5$ or $x = -9$. But it's bad, because the valid result is $x=-9$ or $x=5$ or $x=-2$.
I know another approach that will give appropriate result, but why this one doesn't work?