Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.6 - Radical Equations - Exercise Set - Page 559: 12


$x=-2$ or $x=-1$

Work Step by Step

Add 3 on both sides of the equation to obtain: $x+3=\sqrt{3x+7}$ Square both sides of the equation to obtain: $(x+3)^2=3x+7$ Use the rule $(a+b)^2 = a^2 + 2ab+b^2$ where $a=x$ and $b=3$ to obtain: $\\x^2+6x+9=3x+7$ Move all terms to the left side of the equation. Note that when a term is moved to the other side of the equation, its sign changes to its opposite. $x^2+6x+9-3x-7=0 \\x^2+3x+2=0$ Factor the trinomial to obtain: $(x+2)(x+1)=0$ Equate each factor to zero then solve each equation to obtain: $x+2 = 0 \text{ or } x + 1 = 0 \\x = -2 \text{ or } x = -1$
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