Answer
$x=\{ -9,2 \}$
Work Step by Step
Using the properties of equality, the given expression, $
x^2+7x=18
,$ is equivalent to
\begin{align*}
x^2+7x-18&=0
.\end{align*}
The factored form of the expression above is
\begin{align*}
(x+9)(x-2)&=0
.\end{align*}
Equating each factor to zero (Zero Product Property), then
\begin{align*}
x+9&=0
\\\\\text{ OR }\\\\
x-2&=0
.\end{align*}
Solving each of the equations above results to
\begin{align*}
x+9&=0
\\
x&=-9
\\\\\text{ OR }\\\\
x-2&=0
\\
x&=2
.\end{align*}
Hence, the solutions are $
x=\{ -9,2 \}
.$
