Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.8 - Solving Equations by Factoring and Problem Solving - Exercise Set - Page 323: 58


$y=\left\{ -5,3 \right\}$

Work Step by Step

The factored form of the given expression, $ y^2+(y+2)^2=34 $, is \begin{array}{l} y^2+(y+2)^2=34 \\\\ y^2+y^2+4y+4-34=0 \\\\ 2y^2+4y-30=0 \\\\ y^2+2y-15=0 \\\\ (y+5)(y-3)=0 .\end{array} Equating each factor to zero, then \begin{array}{l} y+5=0 \\ y=0-5 \\ y=-5 ,\text{ OR}\\\\ y-3=0 \\ y=0+3 \\ y=3 \end{array} Hence, $ y=\left\{ -5,3 \right\} $.
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