Answer
$-9 \lt z \lt 4$
Work Step by Step
Given: $x^2+5x-36\lt0$
Let the equation equal 0: $x^2+5x-36=0$
$a=1, b=5, c=-36$
Find $x$ by using:
$x=\frac{-b \pm \sqrt b^2-4ac}{2a}=\frac{-5\pm\sqrt 5^2-4.1.(-36)}{2.1}=\frac{-5\pm13}{2}$
$x=\frac{-5+13}{2}$ or $x=\frac{-5-13}{2}$
$x=4$ or $x=-9$
Since $a \gt 0$ and the inequality sign is $\lt$, the solution region is below and not including the dashed boundary line.
Hence, the solution is $-9 \lt z \lt 4$.
