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: 49



Work Step by Step

Add $6$ to both sides to obtain: $\sqrt{4x+5}=2x-5$ Square both sides to obtain: $4x+5=(2x-5)^2 \\4x+5=(2x)^2-2(2x)(5)+5^2 \\4x+5=4x^2-20x+25$ 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. $0=4x^2-20x+25-4x-5 \\0=4x^2-24x+20 \\4x^2-24x+20=0$ Factor out $4$ to obtain: $4(x^2-6x+5)=0$ Factor the trinomial to obtain: $4(x-5)(x-1)=0$ Divide $4$ to both sides to obtain: $(x-5)(x-1)=0$ Use the zero-factor property by equating each factor to zero. $x-5=0$ or $x-1=0$ Solve each equation to obtain: $x=5$ or $x=1$. Upon checking, only $5$ satisfies the original equation. Thus, the solution to the given equation is $\color{blue}{x=5}$.
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