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: 65

Answer

The solution set is $\left\{-\frac{9}{8}, \frac{9}{8}\right\}$.

Work Step by Step

Add $-81$ to both sides to find: $64x^2-81=0 \\(8x)^2-9^2=0$ 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 find: $(8x-9)(8x+9)=0$ Equate each factor to 0 then solve each equation to find: $8x-9=0 \text{ or } 8x+9=0\\ 8x=9 \text{ or } 8x=-9 \\x=\frac{9}{8} \text{ or } x=-\frac{9}{8}$ The solution set is $\left\{-\frac{9}{8}, \frac{9}{8}\right\}$.
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