Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Section 11.1 - Solving Quadratic Equations by Completing the Square - Practice - Page 759: 6


$y^2-5y+\frac{25}{4} = (y-\frac{5}{2})^2$

Work Step by Step

We add the square of half of the co-efficient of y Co-efficient of y = -5 Half of -5 = $\frac{1}{2} \times -5 = \frac{-5}{2}$ Square of $\frac{-5}{2} = \frac{-5}{2}\times\frac{-5}{2} = \frac{25}{4}$ We add $\frac{25}{4}$ to make $y^2-5y$ a perfect square trinomial. Therefore, $y^2-5y+\frac{25}{4}$ is a perfect square trinomial. Factor form of $y^2-5y+\frac{25}{4}$ = $(y - \frac{5}{2})^2$
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