Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 5 - Review Exercises: 45


$x=\left\{ 0,-\dfrac{3}{2} \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ 6x^2+9x=0 ,$ express the equation in factored form. Next step is to equate each factor to zero (Zero Product Property). Finally, solve each equation. $\bf{\text{Solution Details:}}$ Factoring the $GCF=3x,$ the equation above is equivalent to \begin{array}{l}\require{cancel} 3x(2x+3)=0 .\end{array} Equating each factor to zero (Zero Product Property), the solutions to the equation above are \begin{array}{l}\require{cancel} 3x=0 \\\\\text{OR}\\\\ 2x+3=0 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 3x=0 \\\\ x=\dfrac{0}{3} \\\\ x=0 \\\\\text{OR}\\\\ 2x+3=0 \\\\ 2x=-3 \\\\ x=-\dfrac{3}{2} .\end{array} Hence, $ x=\left\{ 0,-\dfrac{3}{2} \right\} .$
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