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: 2


$\color{blue}{\left\{-3, -2\right\}}$.

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 $a=1, b=5, \text{ and } c= 6$. Substitute these values into the quadratic formula to obtain: \begin{align*} x&=\frac{-5\pm\sqrt{5^2-4(1)(6)}}{2(1)}\\\\ x&=\frac{-5\pm \sqrt{25-24}}{2}\\\\ x&=\frac{-5\pm \sqrt{1}}{2}\\\\ x&=\frac{-5\pm 1}{2}\\\\ \end{align*} Thus, $x_1=\dfrac{-5-1}{2}=\dfrac{-6}{2}=-3\\\\$ $x_2=\dfrac{-5+1}{2}=\dfrac{-4}{2}=-2$ Therefore, the solution set is $\color{blue}{\left\{-3, -2\right\}}$.
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