Answer
$x=-2\pm i\sqrt{3}$
Work Step by Step
Using the properties of equality, the given quadratic equation, $
x^2+4x=-7
,$ is equivalent to
\begin{array}{l}\require{cancel}
x^2+4x+7=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{-4\pm\sqrt{4^2-4(1)(7)}}{2(1)}
\\\\
x=\dfrac{-4\pm\sqrt{16-28}}{2}
\\\\
x=\dfrac{-4\pm\sqrt{-12}}{2}
\\\\
x=\dfrac{-4\pm \sqrt{-1}\cdot\sqrt{12}}{2}
\\\\
x=\dfrac{-4\pm i\cdot\sqrt{4\cdot3}}{2}
\\\\
x=\dfrac{-4\pm i\cdot\sqrt{(2)^2\cdot3}}{2}
\\\\
x=\dfrac{-4\pm2i\sqrt{3}}{2}
\\\\
x=\dfrac{2(-2\pm i\sqrt{3})}{2}
\\\\
x=\dfrac{\cancel{2}(-2\pm i\sqrt{3})}{\cancel{2}}
\\\\
x=-2\pm i\sqrt{3}
.\end{array}
