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: 51

Answer

$y=-\dfrac{1}{2}$

Work Step by Step

The factored form of the given expression, $ y^2+\dfrac{1}{4}=-y $, is \begin{array}{l} y^2+y+\dfrac{1}{4}=0 \\\\ \left( y+\dfrac{1}{2} \right)\left( y+\dfrac{1}{2} \right)=0 \\\\ \left( y+\dfrac{1}{2} \right)\left( y+\dfrac{1}{2} \right)=0 \\\\ \left( y+\dfrac{1}{2} \right)^2=0 .\end{array} Using the Square Root Property, then \begin{array}{l} y+\dfrac{1}{2}=\pm\sqrt{0} \\\\ y+\dfrac{1}{2}=0 \\\\ y=0-\dfrac{1}{2} \\\\ y=-\dfrac{1}{2} \end{array}
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