## College Algebra (11th Edition)

$x=\left\{ -5- i\sqrt{3},-5+ i\sqrt{3} \right\}$
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 $x=\left\{ -5- i\sqrt{3},-5+ i\sqrt{3} \right\} .$