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 - 4.5 Solving Equations by Factoring - 4.5 Exercises - Page 359: 23


$\color{blue}{\left\{-4, 4\right\}}$

Work Step by Step

Factor out $5$ to obtain: $5(x^2-16)=0$ Since $16=4^2$, the given equation can be written as: $5(x^2-4^2)=0$ RECALL: $a^2-b^2=(a-b)(a+b)$ Factor the binomial using the formula above to obtain: $5(x-4)(x+4)=0$ Use the Zero-Factor Property by equating each factor to zero to obtain: $5=0$ or $x-4=0$ or $x+4=0$ Solve each equation to obtain: $5=0$, no solution or $x-4=0 \\x=0+4 \\x=4$ or $x+4=0 \\x=0-4 \\x=-4$ Therefore, the solution set is $\color{blue}{\left\{-4, 4\right\}}$.
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