Chapter 11 - Section 11.2 - Solving Quadratic Equations by Completing the Square - Exercise Set - Page 776: 23

$x=-3\pm2i$

$x^{2}+6x+13=0$ Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a=1$, $b=6$ and $c=13$ Substitute: $x=\dfrac{-6\pm\sqrt{6^{2}-4(1)(13)}}{2(1)}=\dfrac{-6\pm\sqrt{36-52}}{2}=...$ $...=\dfrac{-6\pm\sqrt{-16}}{2}=\dfrac{-6\pm4i}{2}=-3\pm2i$