## Elementary Algebra

$x=-2$
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.