## Intermediate Algebra: Connecting Concepts through Application

$\color{blue}{\left\{-5, -3\right\}}$
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 $a=1, b=8, \text{ and } c= 15$. Substitute these values into the quadratic formula to obtain: \begin{align*} x&=\frac{-8\pm\sqrt{8^2-4(1)(15)}}{2(1)}\\\\ x&=\frac{-8\pm \sqrt{64-60}}{2}\\\\ x&=\frac{-8\pm \sqrt{4}}{2}\\\\ x&=\frac{-8\pm 2}{2}\\\\ \end{align*} Thus, $x_1=\dfrac{-8-2}{2}=\dfrac{-10}{2}=-5\\\\$ $x_2=\dfrac{-8+2}{2}=\dfrac{-6}{2}=-3$ Therefore, the solution set is $\color{blue}{\left\{-5, -3\right\}}$.