## Introductory Algebra for College Students (7th Edition)

$x=\left\{ -7-8i,-7+8i \right\}$
Taking the square root of both sides (the Square Root Property) and using $i=\sqrt{-1}$, the solutions to the given equation, $(x+7)^2=-64 ,$ are \begin{array}{l}\require{cancel} x+7=\pm\sqrt{-64} \\\\ x+7=\pm\sqrt{-1}\cdot\sqrt{64} \\\\ x+7=\pm i\cdot\sqrt{(8)^2} \\\\ x+7=\pm i\cdot8 \\\\ x+7=\pm 8i \\\\ x=-7\pm 8i .\end{array} Hence, $x=\left\{ -7-8i,-7+8i \right\} .$