Answer
$x=\left\{ -5- i\sqrt{3},-5+ i\sqrt{3} \right\}$
Work Step by Step
Taking the square root of both sides, the solutions to the given equation, $
(x+5)^2=-3
,$ are
\begin{array}{l}\require{cancel}
x+5=\pm\sqrt{-3}
\\\\
x+5=\pm\sqrt{-1}\cdot\sqrt{3}
\\\\
x+5=\pm i\sqrt{3}
\\\\
x=-5\pm i\sqrt{3}
.\end{array}
Hence, the solutions are $
x=\left\{ -5- i\sqrt{3},-5+ i\sqrt{3} \right\}
.$
