Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.2 - Factoring the Difference of Two Squares - Problem Set 6.2 - Page 248: 48


The solution set is $\left\{-12, 12\right\}$.

Work Step by Step

Add $-144$ to both sides to obtain: $0=n^2-144 \\0=n^2-12^2$ RECALL: A difference of two squares can be factored using the formula: $a^2-b^2=(a-b)(a+b)$ Factor the difference of two squares to obtain: $0=(n-12)(n+12)$ Equate each factor to 0, and then solve each equation to obtain: $n-12=0 \text{ or } n+12 = 0 \\n=12 \text{ or } n=-12$ The solution set is $\left\{-12, 12\right\}$.
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