Answer
$x=\left\{ -4,1 \right\}$
Work Step by Step
Using the completing the square method, the solutions of the given quadratic equation, $
z^2+3z-4=0
,$ is
\begin{array}{l}\require{cancel}
z^2+3z=4
\\\\
z^2+3z+\left( \dfrac{3}{2}\right)^2=4+\left( \dfrac{3}{2}\right)^2
\\\\
z^2+3z+\dfrac{9}{4}=4+\dfrac{9}{4}
\\\\
\left( z+\dfrac{3}{2}\right)^2=\dfrac{16}{4}+\dfrac{9}{4}
\\\\
\left( z+\dfrac{3}{2}\right)^2=\dfrac{25}{4}
\\\\
z+\dfrac{3}{2}=\pm\sqrt{\dfrac{25}{4}}
\\\\
z+\dfrac{3}{2}=\pm\dfrac{5}{2}
\\\\
z=-\dfrac{3}{2}\pm\dfrac{5}{2}
\\\\
z=\dfrac{-3\pm5}{2}
.\end{array}
Hence, $
x=\left\{ -4,1 \right\}
.$