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: 64

Answer

The solution set is $\left\{-7, 0, 7\right\}$.

Work Step by Step

Factor out $2x$ to find: $2x(x^2-49)=0 \\2x(x^2-7^2)=0$ 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: $2x(x-7)(x+7)=0$ Equate each factor to 0 then solve each equation to find: $2x=0 \text{ or } x-7=0 \text{ or } x+7 = 0\\ x=0 \text{ or } x=7 \text{ or } x=-7$ The solution set is $\left\{-7, 0, 7\right\}$.
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