Answer
$x=\dfrac{-1\pm i\sqrt{11}}{2}$
Work Step by Step
Using the properties of equality, the given quadratic equation, $
x^2+x=-3
,$ is equivalent to
\begin{array}{l}\require{cancel}
x^2+x+3=0
.\end{array}
Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, the solutions of the quadratic equation above are
\begin{array}{l}\require{cancel}
x=\dfrac{-1\pm\sqrt{1^2-4(1)(3)}}{2(1)}
\\\\
x=\dfrac{-1\pm\sqrt{1-12}}{2}
\\\\
x=\dfrac{-1\pm\sqrt{-11}}{2}
\\\\
x=\dfrac{-1\pm\sqrt{-1}\cdot\sqrt{11}}{2}
\\\\
x=\dfrac{-1\pm i\sqrt{11}}{2}
.\end{array}
