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: 63

Answer

The solution set is $\left\{-10, 0, 10\right\}$.

Work Step by Step

Factor out $4x$ to find: $4x(x^2-100)=0 \\4x(x^2-10^2)=0$ 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: $4x(x-10)(x+10)=0$ Equate each factor to 0 then solve each equation to find: $4x=0 \text{ or } x-10=0 \text{ or } x+10 = 0\\ x=0 \text{ or } x=10 \text{ or } x=-10$ The solution set is $\left\{-10, 0, 10\right\}$.
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