Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 4 - Quadratic Functions - 4.5 Solving Equations by Factoring - 4.5 Exercises: 8

Answer

$\color{blue}{\left\{-\frac{5}{2}, 0, \frac{9}{4}\right\}}$

Work Step by Step

RECALL: Zero-Factor Property: If $ab = 0$, then either $a=0$ or $b=0$ or both are $0$. Use the property above to obtain: \begin{array}{ccccc} &-3x=0 &\text{or} &2x+5=0 &\text{or} &4x-9=0 \end{array} Solve each equation to obtain: $-3x=0 \\\frac{-3x}{-3}=\frac{0}{-3} \\x=0$ or $2x+5=0 \\2x=-5 \\\frac{2x}{2}=\frac{-5}{2} \\x=-\frac{5}{2}$ or $4x-9=0 \\4x=0+9 \\4x=9 \\\frac{4x}{4}=\frac{9}{4} \\x=\frac{9}{4}$ Thus, the solution set is $\color{blue}{\left\{-\frac{5}{2}, 0, \frac{9}{4}\right\}}$.
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