Answer
$x=\left\{ -2,1 \right\}$
Work Step by Step
Using the completing the square method, the solutions of the given quadratic equation, $
y^2+y-2=0
,$ is
\begin{array}{l}\require{cancel}
y^2+y=2
\\\\
y^2+y+\left(\dfrac{1}{2}\right)^2=2+\left(\dfrac{1}{2}\right)^2
\\\\
y^2+y+\dfrac{1}{4}=2+\dfrac{1}{4}
\\\\
\left(y+\dfrac{1}{2}\right)^2=\dfrac{8}{4}+\dfrac{1}{4}
\\\\
\left(y+\dfrac{1}{2}\right)^2=\dfrac{9}{4}
\\\\
y+\dfrac{1}{2}=\pm\sqrt{\dfrac{9}{4}}
\\\\
y+\dfrac{1}{2}=\pm\dfrac{3}{2}
\\\\
y=-\dfrac{1}{2}\pm\dfrac{3}{2}
\\\\
y=\dfrac{-1\pm3}{2}
.\end{array}
Hence, $
x=\left\{ -2,1 \right\}
.$
