Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 5 - Polynomials and Factoring - 5.7 Solving Quadratic Equations by Factoring - 5.7 Exercise Set - Page 352: 47


$z=\left\{ -\dfrac{7}{6},\dfrac{7}{6} \right\}$

Work Step by Step

Using the properties of equality, the given expression, $ 36m^2-9=40 ,$ is equivalent to \begin{array}{l}\require{cancel} 36m^2-9-40=0 \\\\ 36m^2-49=0 .\end{array} Factoring the above equation, $ 36m^2-49=0 ,$ results to \begin{array}{l}\require{cancel} (6m+7)(6m-7)=0 .\end{array} Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $ (6m+7)(6m-7)=0 ,$ are \begin{array}{l}\require{cancel} 6m+7=0 \\\\ 6m=-7 \\\\ m=-\dfrac{7}{6} ,\\\\\text{OR}\\\\ 6m-7=0 \\\\ 6m=7 \\\\ m=\dfrac{7}{6} .\end{array} Hence, $ z=\left\{ -\dfrac{7}{6},\dfrac{7}{6} \right\} .$
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