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

Published by Pearson

Chapter 5 - Polynomials and Factoring - 5.7 Solving Quadratic Equations by Factoring - 5.7 Exercise Set - Page 352: 44

Answer

$x=\left\{ 1,4 \right\}$

Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$ or the Distributive Property, the given expression, $(x+2)(x-7)=-18 ,$ is equivalent to \begin{array}{l}\require{cancel} x(x)+x(-7)+2(x)+2(-7)=-18 \\\\ x^2-7x+2x-14=-18 \\\\ x^2-7x+2x-14+18=0 \\\\ x^2-5x+4=0 .\end{array} Factoring the above equation, $x^2-5x+4=0 ,$ results to \begin{array}{l}\require{cancel} (x-4)(x-1)=0 .\end{array} Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $(x-4)(x-1)=0 ,$ are \begin{array}{l}\require{cancel} x-4=0 \\\\ x=4 ,\\\\\text{OR}\\\\ x-1=0 \\\\ x=1 .\end{array} Hence, $x=\left\{ 1,4 \right\} .$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.