#### Answer

$x_{1}=6$ and $x_{2}=-11$

#### Work Step by Step

Given $x(x+5)=66 \longrightarrow x^2+5x-66=0$
$a= 1, \ b=5, \ c=-66$
Using the quadratic formula: $\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$ we have:
$\dfrac{-5 \pm \sqrt{5^2-4 \times 1\times (-66)}}{2 \times 1} = \dfrac{-5 \pm \sqrt{25+264}}{2} = \dfrac{-5 \pm \sqrt{289}}{2} = \dfrac{-5 \pm 17}{2}$
Therefore the solutions are $x_{1}=\dfrac{-5 + 17}{2}=\dfrac{12}{2}=6$ and $x_{2} = \dfrac{-5 - 17}{2} = \dfrac{-22}{2}=-11$