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: 24


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

Work Step by Step

Factor out $-3$ to obtain: $-3(m^2-25)=0$ Since $25=5^2$, the given equation can be written as: $-3(m^2-5^2)=0$ RECALL: $a^2-b^2=(a-b)(a+b)$ Factor the binomial using the formula above to obtain: $-3(m-5)(m+5)=0$ Use the Zero-Factor Property by equating each factor to zero to obtain: $-3=0$ or $m-5=0$ or $m+5=0$ Solve each equation to obtain: $-3=0$, no solution or $m-5=0 \\m=0+5 \\m=5$ or $m+5=0 \\m=0-5 \\m=-5$ Therefore, the solution set is $\color{blue}{\left\{-5, 5\right\}}$.
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