Answer
$x=\left\{ -2-i\sqrt{2},-2+i\sqrt{2} \right\}$
Work Step by Step
Using the completing the square method, the solutions of the given quadratic equation, $
x^2+4x+6=0
,$ is
\begin{array}{l}\require{cancel}
x^2+4x=-6
\\\\
x^2+4x+\left( \dfrac{4}{2} \right)^2=-6+\left( \dfrac{4}{2} \right)^2
\\\\
x^2+4x+4=-6+4
\\\\
(x+2)^2=-2
\\\\
x+2=\pm\sqrt{-2}
\\\\
x+2=\pm i\sqrt{2}
\\\\
x=-2\pm i\sqrt{2}
.\end{array}
Hence, $
x=\left\{ -2-i\sqrt{2},-2+i\sqrt{2} \right\}
.$
