Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 9 - Section 9.1 - Solving Quadratic Equations by the Square Root Property - Exercise Set: 31

Answer

$x=\{−6,2\}$

Work Step by Step

The left side of the given equation, $x^2+4x+4=16$, is a perfect square trinomial whose factored form is $(x+2)^2=16$. Taking the square root of both sides (the Square Root Property), the solutions to the given equation are $x+2=\pm\sqrt {16}$ $x+2=\pm\sqrt {(4)2}$ $x+2=\pm4$ $x=−2+4$ or $x=-2-4$ $x=2$ or $x=-6$ Hence, $x=\{−6,2\}$.
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