Answer
$x=-6,\text{ }11$
Work Step by Step
In the form $ax^2+bx+c=0,$ the given equation, $
x(x-5)=66
,$ is equivalent to
\begin{align*}
x(x)+x(-5)&=66
&(\text{use Distributive Property})
\\
x^2-5x&=66
\\
x^2-5x-66&=0
.\end{align*}
Using the factoring of quadratic trinomials, the factored form of the equation above is
\begin{align*}
(x-11)(x+6)&=0
.\end{align*}
Equating each factor to zero (Zero Product Property) and solving for the variable, then
\begin{align*}
x-11&=0
\\
x&=11
\\\\\text{OR}\\\\
x+6&=0
\\
x&=-6
.\end{align*}
Hence, the solutions to the equation $
x(x-5)=66
$ are $
x=-6,\text{ }11
.$
