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 - Exercise Set: 32

Answer

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

Work Step by Step

We add the square of half of the coefficent of $n$ so that the result is a perfect square trinomial. Co-efficient of $n=5$ Half of 5 is $\frac{1}{2}×5=\frac{5}{2}$ Square of $\frac{5}{2}$ is $\frac{5}{2}×\frac{5}{2}=\frac{25}{4}$ We add $\frac{25}{4}$ to $n^2+5n$ to make it a perfect square trinomial. Hence it becomes $n^2+5n+\frac{25}{4}$ Factored form- $n^2+5n+\frac{25}{4}$ $= n^2+\frac{5}{2}n+\frac{5}{2}n +\frac{25}{4} $ $=n(n+\frac{5}{2})+\frac{5}{2} (n+\frac{5}{2})$ (Taking the common factors) $=(n+\frac{5}{2}) (n+\frac{5}{2})$ ($(n+\frac{5}{2})$ is taken common from both the terms) $=(n+\frac{5}{2})^2$
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