Answer
$-1\pm 2i$
Work Step by Step
$x^{2}+2x+5=0$
We solve using the quadratic formula (a=1, b=2, c=5):
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$x=\displaystyle \frac{-2\pm\sqrt{2^{2}-4(1)(5)}}{2(1)}$
$=\frac{-2\pm\sqrt{-16}}{2}$
$=\frac{-2\pm\sqrt{-1*16}}{2}$
We use the fact that $\sqrt{-1}=i$:
$=\frac{-2\pm 4i}{2}$
$=-1\pm 2i$
