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 - Page 147: 50


$\color{blue}{x=3, x=-1}$

Work Step by Step

Add $9$ to both sides to obtain: $\sqrt{6x+7}=x+2$ Square both sides to obtain: $6x+7=(x+2)^2 \\6x+7=x^2+2(x)(2)+2^2 \\6x+7=x^2+4x+4$ 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. $0=x^2+4x+4-6x-7 \\0=x^2-2x-3 \\x^2-2x-3=0$ Factor the trinomial to obtain: $(x-3)(x+1)=0$ Use the zero-factor property by equating each factor to zero. $x-3=0$ or $x+1=0$ Solve each equation to obtain: $x=3$ or $x=-1$. Upon checking, both proposed solutions satisfy the original equation. Thus, the solutions to the given equation are $\color{blue}{x=3, x=-1}$.
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