#### Answer

$-3\pm i$

#### Work Step by Step

$x^{2}+6x+10=0$
We use the quadratic formula ($a=1, b=6, c=10$):
$x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}=\frac{-6\pm\sqrt{6^{2}-4*1*10}}{2*1}=\frac{-6\pm\sqrt{36-40}}{2}=\frac{-6\pm\sqrt{-4}}{2}=\frac{-6\pm2i}{2}=-3\pm i$