Answer
$x=-1\pm i$
Work Step by Step
$x^{2}+2x+2=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=1$, $b=2$ and $c=2$.
Substitute the known values in the formula:
$x=\dfrac{-2\pm\sqrt{2^{2}-4(1)(2)}}{2(1)}=\dfrac{-2\pm\sqrt{4-8}}{2}=...$
$...=\dfrac{-2\pm\sqrt{-4}}{2}=\dfrac{-2\pm2i}{2}=-1\pm i$
The solution is $x=-1\pm i$
