Answer
$-\frac{1}{2}+\frac{\sqrt{2}}{2}i$
Work Step by Step
Original Problem:
$\frac{-5+\sqrt{-50}}{10}$
Factor out 5 and $\sqrt{1}$ from $\sqrt{-50}$.
$\frac{-5+\sqrt{-1}\times5\sqrt{2}}{10}$
Recall that $\sqrt{-1}$ = $i$.
$\frac{-5+5i\sqrt{2}}{10}$
Simplify.
$\frac{-1+i\sqrt{2}}{2}$
Separate.
$-\frac{1}{2}+\frac{\sqrt{2}}{2}i$