College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Section 1.4 - Quadratic Equations - 1.4 Exercises - Page 112: 33


$x=\left\{ -5- i\sqrt{3},-5+ i\sqrt{3} \right\}$

Work Step by Step

Taking the square root of both sides, the solutions to the given equation, $ (x+5)^2=-3 ,$ are \begin{array}{l}\require{cancel} x+5=\pm\sqrt{-3} \\\\ x+5=\pm\sqrt{-1}\cdot\sqrt{3} \\\\ x+5=\pm i\sqrt{3} \\\\ x=-5\pm i\sqrt{3} .\end{array} Hence, the solutions are $ x=\left\{ -5- i\sqrt{3},-5+ i\sqrt{3} \right\} .$
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