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: 57

Answer

$x=\left\{ -6,5 \right\}$

Work Step by Step

The factored form of the given expression, $ x^2+(x+1)^2=61 $, is \begin{array}{l} x^2+x^2+2x+1-61=0 \\\\ 2x^2+2x-60=0 \\\\ x^2+x-30=0 \\\\ (x+6)(x-5)=0 .\end{array} Equating each factor to zero, then \begin{array}{l} x+6=0 \\ x=0-6 \\ x=-6 ,\text{ OR}\\\\ x-5=0 \\ x=0+5 \\ x=5 \end{array} Hence, $ x=\left\{ -6,5 \right\} $.
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