Answer
$\displaystyle -\frac{1}{4}\pm\frac{\sqrt{15}}{4}i$
Work Step by Step
$\displaystyle x^{2}+\frac{1}{2}x+1=0$
We use the quadratic formula ($a=1, b=1/2, c=1$):
$x=\displaystyle \frac{-\frac{1}{2}\pm\sqrt{(\frac{1}{2})^{2}-4*1*1}}{2(1)}=\frac{-\frac{1}{2}\pm\sqrt{\frac{1}{4}-\frac{16}{4}}}{2}=\frac{-\frac{1}{2}\pm\sqrt{-\frac{15}{4}}}{2}=\frac{-\frac{1}{2}\pm\frac{1}{2}\sqrt{15}i}{2}=-\frac{1}{4}\pm\frac{\sqrt{15}}{4}i$
