Answer
$x=-\dfrac{1}{4}\pm\dfrac{\sqrt{15}}{4}i$
Work Step by Step
$x^{2}+\dfrac{1}{2}x+1=0$
Multiply the whole equation by $2$:
$2\Big(x^{2}+\dfrac{1}{2}x+1=0\Big)$
$2x^{2}+x+2=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=2$, $b=1$ and $c=2$.
Substitute the known values in the formula:
$x=\dfrac{-1\pm\sqrt{1^{2}-4(2)(2)}}{2(2)}=\dfrac{-1\pm\sqrt{1-16}}{4}=...$
$...=\dfrac{-1\pm\sqrt{-15}}{4}=\dfrac{-1\pm\sqrt{15}i}{4}=-\dfrac{1}{4}\pm\dfrac{\sqrt{15}}{4}i$
The answer is $x=-\dfrac{1}{4}\pm\dfrac{\sqrt{15}}{4}i$
