Answer
$x=-7\pm\sqrt{29}$
Work Step by Step
Using the completing the square method, the solutions of the given quadratic equation, $
x^2+14x+20=0
,$ is
\begin{array}{l}\require{cancel}
x^2+14x=-20
\\\\
x^2+14x+\left( \dfrac{14}{2} \right)^2=-20+\left( \dfrac{14}{2} \right)^2
\\\\
x^2+14x+49=-20+49
\\\\
(x+7)^2=29
\\\\
x+7=\pm\sqrt{29}
\\\\
x=-7\pm\sqrt{29}
.\end{array}