College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Review Exercises - Page 163: 40


$x=\left\{ \dfrac{1}{6},\dfrac{1}{2} \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ 12x^2=8x-1 ,$ express first in the form $ax^2+bx+c=0.$ Then factor the left side. Equate each factor to zero (Zero Product Property). Finally, use the properties of equality to isolate the variable in each equation. $\bf{\text{Solution Details:}}$ In the form $ax^2+bx+c=0,$ the given equation is equivalent to \begin{array}{l}\require{cancel} 12x^2-8x+1=0 .\end{array} Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the factored form of equation above is \begin{array}{l}\require{cancel} (2x-1)(6x-1)=0 .\end{array} Equating each factor to zero (Zero Product Property), then \begin{array}{l}\require{cancel} 2x-1=0 \\\\\text{OR}\\\\ 6x-1=0 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 2x-1=0 \\\\ 2x=1 \\\\ x=\dfrac{1}{2} \\\\\text{OR}\\\\ 6x-1=0 \\\\ 6x=1 \\\\ x=\dfrac{1}{6} .\end{array} Hence, the solutions are $ x=\left\{ \dfrac{1}{6},\dfrac{1}{2} \right\} .$
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