Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 4 - Quadratic Functions - 4.6 Solving Quadratic Equations by Using the Quadratic Formula - 4.6 Exercises - Page 372: 1


$\color{blue}{\left\{-5, -3\right\}}$

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 $a=1, b=8, \text{ and } c= 15$. 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 $\color{blue}{\left\{-5, -3\right\}}$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.