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: 22


$\color{blue}{\left\{-8, 8\right\}}$

Work Step by Step

RECALL: $a^2-b^2=(a-b)(a+b)$ Since $64=8^2$, the given equation can be written as: $t^2-8^2=0$ Factor the binomial using the formula above to obtain: $(t-8)(t+8)=0$ Use the Zero-Factor Property by equating each factor to zero to obtain: $t-8=0$ or $t+8=0$ Solve each equation to obtain: $t-8=0 \\t=0+8 \\t=8$ or $t+8=0 \\t=0-8 \\t=-8$ Therefore, the solution set is $\color{blue}{\left\{-8, 8\right\}}$.
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