Answer
$\left\{-4,9\right\}$
Work Step by Step
Using factoring of trinomials, the given equation, $
x^2-5x-36=0
,$ is equivalent to
\begin{align*}
(x-9)(x+4)&=0
.\end{align*}
Equating each factor to zero (Zero Product Property) and solving for the variable, then
\begin{array}{l|r}
x-9=0 & x+4=0
\\
x=9 & x=-4
.\end{array}
Hence, the solution set of the equation $
x^2-5x-36=0
$ is $\left\{-4,9\right\}$.
