Chapter 11 - Section 11.2 - Solving Quadratic Equations by Completing the Square - Exercise Set - Page 776: 24

$x=-1\pm i$

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