Answer
$x=\left\{ 4-i\sqrt{5},4+ i\sqrt{5} \right\}$
Work Step by Step
Taking the square root of both sides, the solutions to the given equation, $
(x-4)^2=-5
,$ are
\begin{array}{l}\require{cancel}
x-4=\pm\sqrt{-5}
\\\\
x-4=\pm\sqrt{-1}\cdot\sqrt{5}
\\\\
x-4=\pm i\sqrt{5}
\\\\
x=4\pm i\sqrt{5}
.\end{array}
Hence, the solutions are $
x=\left\{ 4-i\sqrt{5},4+ i\sqrt{5} \right\}
.$
