Answer
$x=\left\{ -5-i\sqrt{3},-5+i\sqrt{3} \right\}$
Work Step by Step
Using the completing the square method, the solutions of the given quadratic equation, $
x^2+10x+28=0
,$ is
\begin{array}{l}\require{cancel}
x^2+10x=-28
\\\\
x^2+10x+\left( \dfrac{10}{2} \right)^2=-28+\left( \dfrac{10}{2} \right)^2
\\\\
x^2+10x+25=-28+25
\\\\
(x+5)^2=-3
\\\\
x+5=\pm\sqrt{-3}
\\\\
x+5=\pm i\sqrt{3}
\\\\
x=-5\pm i\sqrt{3}
.\end{array}
Hence, $
x=\left\{ -5-i\sqrt{3},-5+i\sqrt{3} \right\}
.$