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: 55


The solution set is $\left\{-5, 5\right\}$.

Work Step by Step

Divide 3 to both sides to obtain: $x^2 = 25$ Add $-25$ to both sides to obtain: $x^2-25 = 0 \\x^2-5^2=0$ 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: $(x-5)(x+5)=0$ Equate each factor to 0, and then solve each equation to have: $x-5=0 \text{ or } x+5 = 0 x=5 \text{ or } x=-5$ The solution set is $\left\{-5, 5\right\}$.
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