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: 37

Answer

$x=\left\{ 8 \right\}$

Work Step by Step

Factoring the given equation, $ 64+x^2=16x ,$ results to \begin{array}{l}\require{cancel} x^2-16x+64=0 \\\\ (x-8)^2=0 \\\\ (x-8)(x-8)=0 .\end{array} Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $ (x-8)(x-8)=0 ,$ are \begin{array}{l}\require{cancel} x-8=0 \\\\ x=8 ,\\\\\text{OR}\\\\ x-8=0 \\\\ x=8 .\end{array} Hence, $ x=\left\{ 8 \right\} .$
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