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: 21


$x=\left\{ 2-i\sqrt{7},2+ i\sqrt{7} \right\}$

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-2)^2=-7 ,$ are \begin{array}{l}\require{cancel} x-2=\pm\sqrt{-7} \\\\ x-2=\pm\sqrt{-1}\cdot\sqrt{7} \\\\ x-2=\pm i\sqrt{7} \\\\ x=2\pm i\sqrt{7} .\end{array} Hence, $ x=\left\{ 2-i\sqrt{7},2+ i\sqrt{7} \right\} .$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.