Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 11 - Quadratic Functions and Equations - 11.1 Quadratic Equations - 11.1 Exercise Set: 26

Answer

$x=1\pm 7i$

Work Step by Step

Since $x^2=a$ implies $x=\pm\sqrt{a}$ (the Square Root Principle), the solutions to the given equation, $ (x-1)^2=-49 ,$ are \begin{array}{l}\require{cancel} x-1=\pm\sqrt{-49} \\\\ x-1=\pm\sqrt{-1}\cdot\sqrt{49} \\\\ x-1=\pm i\cdot\sqrt{(7)^2} \\\\ x-1=\pm i\cdot7 \\\\ x-1=\pm 7i \\\\ x=1\pm 7i .\end{array}
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