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

$x=\left\{ -12-10i,-12+10i \right\}$
Taking the square root of both sides (the Square Root Property) and using $i=\sqrt{-1}$, the solutions to the given equation, $(x+12)^2=-100 ,$ are \begin{array}{l}\require{cancel} x+12=\pm\sqrt{-100} \\\\ x+12=\pm\sqrt{-1}\cdot\sqrt{100} \\\\ x+12=\pm i\cdot\sqrt{(10)^2} \\\\ x+12=\pm i\cdot10 \\\\ x+12=\pm 10i \\\\ x=-12\pm 10i .\end{array} Hence, $x=\left\{ -12-10i,-12+10i \right\} .$