Answer
$x=-1\pm\sqrt{6}$
Work Step by Step
Using the completing the square method, then,
\begin{array}{l}
x^2+2x-5=0\\
x^2+2x=5\\
x^2+2x+\left( \dfrac{2}{2} \right)^2=5+\left( \dfrac{2}{2}\right)^2\\
x^2+2x+1=5+1\\
\left( x+1 \right)^2=6\\
x+1=\pm\sqrt{6}\\
x=-1\pm\sqrt{6}
.\end{array}
