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 R - Elementary Algebra Review - R.5 Polynomials and Factoring - R.5 Exercise Set: 36

Answer

$x=\left\{ 0,\dfrac{1}{4} \right\}$

Work Step by Step

Using the properties of equality, the given equation is equivalent to \begin{array}{l}\require{cancel} 8x^2=2x \\\\ 8x^2-2x=0 .\end{array} Factoring the $GCF=2x,$ the equation above is equivalent to \begin{array}{l}\require{cancel} 8x^2-2x=0 \\\\ 2x(4x-1)=0 .\end{array} Equating each factor to zero (Zero Product Property), then \begin{array}{l}\require{cancel} 2x=0 \\\\\text{OR}\\\\ 4x-1=0 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 2x=0 \\\\ x=\dfrac{0}{2} \\\\ x=0 \\\\\text{OR}\\\\ 4x-1=0 \\\\ 4x=1 \\\\ x=\dfrac{1}{4} .\end{array} Hence, the solutions are $ x=\left\{ 0,\dfrac{1}{4} \right\} .$
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