Answer
$m=\dfrac{1\pm i\sqrt{31}}{2}$
Work Step by Step
Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), the solution/s of the given equation, $
m^2-m+8=0
,$ is/are
\begin{array}{l}\require{cancel}
m=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(1)(8)}}{2(1)}
\\\\
m=\dfrac{1\pm\sqrt{1-32}}{2}
\\\\
m=\dfrac{1\pm\sqrt{-31}}{2}
\\\\
m=\dfrac{1\pm\sqrt{-1}\cdot\sqrt{31}}{2}
\\\\
m=\dfrac{1\pm i\sqrt{31}}{2}
.\end{array}
