Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.4 Quadratic Equations - 1.4 Exercises - Page 121: 33


$\color{blue}{\left\{-5-i\sqrt3, -5+i\sqrt3\right\}}$

Work Step by Step

RECALL: If $x^2=a$, then taking the square root of both sides gives $x = \pm \sqrt{a}$. Take the square root of both sides of the given equation to obtain: $\sqrt{(x+5)^2}=\pm \sqrt{-3} \\x+5 =\pm \sqrt{-1(3)}$ Since $\sqrt{-1}=i$, then the expression above is equivalent to: $x+5=\pm i\sqrt{3}$ Subtract $5$ to both sides: $x =-5 \pm i\sqrt{3}$ Thus, the solution set is $\color{blue}{\left\{-5-i\sqrt3, -5+i\sqrt3\right\}}$.
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