Answer
$x=-\dfrac{3}{2}\pm\dfrac{\sqrt{19}}{2}i$
Work Step by Step
$x^{2}+3x+7=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=1$, $b=3$ and $c=7$.
Substitute the known values in the formula:
$x=\dfrac{-3\pm\sqrt{3^{2}-4(1)(7)}}{2(1)}=\dfrac{-3\pm\sqrt{9-28}}{2}=\dfrac{-3\pm\sqrt{-19}}{2}=...$
$...=\dfrac{-3\pm\sqrt{19}i}{2}=-\dfrac{3}{2}\pm\dfrac{\sqrt{19}}{2}i$
The answer is $x=-\dfrac{3}{2}\pm\dfrac{\sqrt{19}}{2}i$
