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: 23

Answer

$t=-5\pm2\sqrt{3}$

Work Step by Step

Since $x^2=a$ implies $x=\pm\sqrt{a}$ (the Square Root Principle), the solutions to the given equation, $ (t+5)^2=12 ,$ are \begin{array}{l}\require{cancel} t+5=\pm\sqrt{12} \\\\ t+5=\pm\sqrt{4\cdot3} \\\\ t+5=\pm\sqrt{(2)^2\cdot3} \\\\ t+5=\pm2\sqrt{3} \\\\ t=-5\pm2\sqrt{3} .\end{array}
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