Answer
$x=\left\{ -6,-3 \right\}$
Work Step by Step
The factored form of the given expression, $
\dfrac{x^2}{18}+\dfrac{x}{2}+1=0
$, is
\begin{array}{}
18\left( \dfrac{x^2}{18}+\dfrac{x}{2}+1 \right)=(0)18
\\\\
1(x^2)+9(x)+18(1)=0
\\\\
x^2+9x+18=0
\\\\
(x+6)(x+3)=0
.\end{array}
Equating each factor to zero, then
\begin{array}{l}
x+6=0
\\
x=0-6
\\
x=-6
,\text{ OR}\\\\
x+3=0
\\
x=0-3
\\
x=-3
\end{array}
Hence, $
x=\left\{ -6,-3 \right\}
$.
