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: 52

Answer

$x=\left\{ -2,9 \right\}$

Work Step by Step

Using the properties of equality, the given expression, $ x^2-2x=18+5x ,$ is equivalent to \begin{array}{l}\require{cancel} x^2-2x-5x-18=0 \\\\ x^2-7x-18=0 .\end{array} Factoring the above equation, $ x^2-7x-18=0 ,$ results to \begin{array}{l}\require{cancel} (x-9)(x+2)=0 .\end{array} Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $ (x-9)(x+2)=0 ,$ are \begin{array}{l}\require{cancel} x-9=0 \\\\ x=9 ,\\\\\text{OR}\\\\ x+2=0 \\\\ x=-2 .\end{array} Hence, $ x=\left\{ -2,9 \right\} .$
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