Answer
$\left\{ -1-i,-1+i \right\}$
Work Step by Step
Using $\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), the solutions of the given quadratic equation, $
x^2+2x+2=0
,$ are
\begin{array}{l}\require{cancel}
\dfrac{-(2)\pm\sqrt{(2)^2-4(1)(2)}}{2(1)}
\\\\=
\dfrac{-2\pm\sqrt{4-8}}{2}
\\\\=
\dfrac{-2\pm\sqrt{-4}}{2}
\\\\=
\dfrac{-2\pm\sqrt{4}\cdot\sqrt{-1}}{2}
\\\\=
\dfrac{-2\pm\sqrt{(2)^2}\cdot i}{2}
\\\\=
\dfrac{-2\pm2i}{2}
\\\\=
\dfrac{2(-1\pm i)}{2}
\\\\=
\dfrac{\cancel{2}(-1\pm i)}{\cancel{2}}
\\\\=
-1\pm i
.\end{array}
Hence, the solutions are $
\left\{ -1-i,-1+i \right\}
.$
