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 - Page 359: 29


$\color{blue}{\left\{0, \frac{5}{3}\right\}}$

Work Step by Step

Subtract $10x$ to both sides of the equation to obtain: $6x^2-10x=10x-10x \\6x^2-10x=0$ Factor out $x$ to obtain: $x(6x-10)=0$ RECALL: The Zero-Factor Property states that if $ab=0$, then $a=0$ or $b=0$, or both are zero. Use the Zero-Factor Property by equating each factor to zero to obtain: $x=0$ or $6x-10=0$ Solve each equation to obtain: $x=0$ or $6x-10=0 \\6x=0+10 \\6x=10 \\\frac{6x}{6}=\frac{10}{6} \\x=\frac{5}{3}$ Therefore, the solution set is $\color{blue}{\left\{0, \frac{5}{3}\right\}}$.
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