Answer
$\color{blue}{\left\{-\frac{21}{5}, 2\right\}}$
Work Step by Step
The solutions of the quadratic equation $ax^2+bx+c=0$ can be found using the quadratic formula:
$$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$$
The given quadratic equation has $a=5, b=11, \text{ and } c= -425$.
Substitute these values into the quadratic formula to obtain:
\begin{align*}
x&=\frac{-11\pm\sqrt{11^2-4(5)(-42)}}{2(5)}\\\\
x&=\frac{-11\pm \sqrt{121+840}}{10}\\\\
x&=\frac{-11\pm \sqrt{961}}{10}\\\\
x&=\frac{-11\pm 31}{10}\\\\
\end{align*}
Thus,
$x_1=\dfrac{-11+31}{10}=\dfrac{20}{10}=2\\\\$
$x_2=\dfrac{-11-31}{10}=\dfrac{-42}{10}=-\dfrac{21}{5}$
Therefore, the solution set is $\color{blue}{\left\{-\frac{21}{5}, 2\right\}}$.
