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: 18


$x=\left\{ 5-6i,5+6i \right\}$

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-5)^2=-36 ,$ are \begin{array}{l}\require{cancel} x-5=\pm\sqrt{-36} \\\\ x-5=\pm\sqrt{-1}\cdot\sqrt{36} \\\\ x-5=\pm i\cdot\sqrt{(6)^2} \\\\ x-5=\pm i\cdot6 \\\\ x-5=\pm 6i \\\\ x=5\pm 6i .\end{array} Hence, $ x=\left\{ 5-6i,5+6i \right\} .$
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