Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.6 Other Types of Equations and Applications - 1.6 Exercises: 47

Answer

$\color{blue}{x=-1}$

Work Step by Step

Square both sides to obtain: $3x+7=(3x+5)^2 \\3x+7=(3x)^2+2(3x)(5)+5^2 \\3x+7=9x^2+30x+25$ Move all terms to the left side of the equation. Note that when a term is transferred to the other side of the equation, its sign changes to its opposite. $0=9x^2+30x+25-3x-7 \\0=9x^2+27x+18 \\9x^2+27x+18=0$ Factor out $9$ to obtain: $9(x^2+3x+2)=0$ Factor the trinomial to obtain: $9(x+2)(x+1)=0$ Divide $9$ to both sides to obtain: $(x+2)(x+1)=0$ Use the zero-factor property by equating each factor to zero. $x+2=0$ or $x+1=0$ Solve each equation to obtain: $x=-2$ or $x=-1$. Upon checking, only $-1$ is a solution of the original equation. Thus, the solution to the given equation is $\color{blue}{x=-1}$.
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