$\displaystyle -2 + \frac{\sqrt{-100}}{2} $

the correct answer is $\displaystyle -1 + 5i $

here's my work out;

$\displaystyle -1 + {\sqrt{-50} $ =

$\displaystyle -1 + \sqrt{50} \times \sqrt{-1} $ =

$\displaystyle -1 + \sqrt{25} \times \sqrt{2} i $

$\displaystyle -1 + 5\sqrt{2}i $

Can someone please show me where I have gone wrong? Thank you.