Answer
$x=\dfrac{-1\pm 3i\sqrt{3}}{2}$
Work Step by Step
Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, the solution/s of the given quadratic equation, $
x^2+x+7=0
,$ is/are
\begin{array}{l}\require{cancel}
x=\dfrac{-1\pm\sqrt{1^2-4(1)(7)}}{2(1)}
\\\\
x=\dfrac{-1\pm\sqrt{1-28}}{2}
\\\\
x=\dfrac{-1\pm\sqrt{-27}}{2}
\\\\
x=\dfrac{-1\pm\sqrt{-1}\cdot\sqrt{27}}{2}
\\\\
x=\dfrac{-1\pm i\cdot\sqrt{9\cdot3}}{2}
\\\\
x=\dfrac{-1\pm i\cdot3\sqrt{3}}{2}
\\\\
x=\dfrac{-1\pm 3i\sqrt{3}}{2}
.\end{array}
