Answer
$-11$; $6$
Work Step by Step
Given \begin{equation}
3 x^2+15 x=198.
\end{equation} Apply the method of completing the square to solve for $x$. Make sure that the coefficient of the square term is one before adding half the square of the coefficient of the $x$ term to both sides. First divide each side by $3$: \begin{equation}
\begin{aligned}
\frac{3 x^2+15 x}{3} & =\frac{198}{3} \\
x^2+5x&=66\\
x^2+2\cdot 2.5x+2.5^2 & =66+2.5^2 \\
(x+2.5)^2 & =72.25 \\
x+2.5 & = \pm \sqrt{72.25} \\
x & =-2.5 \pm 8.5
\end{aligned}
\end{equation} This gives: \begin{equation}
\begin{aligned}
x & =-2.5-8.5 \\
& =-11 \\
x & =-2.5+8.5 \\
& =6.
\end{aligned}
\end{equation} Check: \begin{equation}
\begin{array}{r}
3 \cdot (-11)^2+15(-11)\stackrel{?}{=}198 \\
198=198\checkmark\\
3 \cdot (6)^2+15(6)\stackrel{?}{=}198 \\
198=198\checkmark.
\end{array}
\end{equation} The solution is $$x=-11,\quad x=6.$$
