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: 54

Answer

The solution set is $\left\{-\frac{6}{7}, \frac{6}{7}\right\}$.

Work Step by Step

Add $-36$ to both sides to obtain: $49x^2-36=0 (7x)^2-6^2=0$ 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 obtain: $(7x-6)(7x+6)=0$ Equate each factor to 0, and then solve each equation to obtain: $7x-6=0 \text{ or } 7x+6 = 0 \\7x=6 \text{ or } 7x=-6 \\x=\frac{6}{7} \text{ or } x=-\frac{6}{7}$ The solution set is $\left\{-\frac{6}{7}, \frac{6}{7}\right\}$.
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