Answer
$x=\left\{ \dfrac{5-2i\sqrt{2}}{2},\dfrac{5+2i\sqrt{2}}{2} \right\}
$
Work Step by Step
Taking the square root of both sides, the solutions to the given equation, $
(-2x+5)^2=-8
,$ are
\begin{array}{l}\require{cancel}
-2x+5=\pm\sqrt{-8}
\\\\
-2x+5=\pm\sqrt{-1}\cdot\sqrt{8}
\\\\
-2x+5=\pm i\sqrt{4\cdot2}
\\\\
-2x+5=\pm i\sqrt{(2)^2\cdot2}
\\\\
-2x+5=\pm 2i\sqrt{2}
\\\\
-2x=-5\pm 2i\sqrt{2}
\\\\
x=\dfrac{-5\pm 2i\sqrt{2}}{-2}
\\\\
x=\dfrac{5\pm 2i\sqrt{2}}{2}
.\end{array}
Hence, the solutions are $
x=\left\{ \dfrac{5-2i\sqrt{2}}{2},\dfrac{5+2i\sqrt{2}}{2} \right\}
.$
