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 9.4 - Imaginary Numbers as Solutions of Quadratic Equations - Exercise Set - Page 655: 19


$x=\left\{ -7-8i,-7+8i \right\}$

Work Step by Step

Taking the square root of both sides (the Square Root Property) and using $i=\sqrt{-1}$, the solutions to the given equation, $ (x+7)^2=-64 ,$ are \begin{array}{l}\require{cancel} x+7=\pm\sqrt{-64} \\\\ x+7=\pm\sqrt{-1}\cdot\sqrt{64} \\\\ x+7=\pm i\cdot\sqrt{(8)^2} \\\\ x+7=\pm i\cdot8 \\\\ x+7=\pm 8i \\\\ x=-7\pm 8i .\end{array} Hence, $ x=\left\{ -7-8i,-7+8i \right\} .$
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