Question:
$x^{2}+2 x+2=0$
Solution:
Given:
$x^{2}+2 x+2=0$
Solution of a general quadratic equation $a x^{2}+b x+c=0$ is given by:
$x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$
$\Rightarrow x=\frac{-2 \pm \sqrt{(2)^{2}-(4 \times 1 \times 2)}}{2 \times 1}$
$\Rightarrow x=\frac{-2 \pm \sqrt{4-8}}{2}$
$\Rightarrow \quad x=\frac{-2 \pm \sqrt{-4}}{2}$
$\Rightarrow x=\frac{-2 \pm 2 i}{2}$
$\Rightarrow x=-\frac{2}{2} \pm \frac{2}{2} i$
$\Rightarrow^{x}=-1 \pm i$
Ans: $x=-1+i$ and $x=-1-i$