Answer
$x=-2$
Work Step by Step
Squaring both sides of the equation and then using the properties of equality, we obtain:
\begin{array}{l}\require{cancel}\left(
\sqrt{-2x}
\right)^2=\left(
x+4
\right)^2
\\\\
-2x=(x)^2+2(x)(4)+(4)^2
\\\\
-2x=x^2+8x+16
\\\\
0=x^2+(8x+2x)+16
\\\\
x^2+10x+16=0
\\\\
(x+8)(x+2)=0
\\\\
x=\{-8,-2\}
.\end{array}
Upon checking, only $
x=-2
$ satisfies the original equation.
