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: 27

Answer

$x^{2}+16x+64= (x+8)^2$

Work Step by Step

We add the square of half of the co-efficent of $x$ so that the result is a perfect square trinomial. Co-efficient of $x=16$ Half of 16 is $16×\frac{1}{2}=8$ Square of is $8×8=64$ We add 64 to $x^2+16x$ to make it a perfect square trinomial. Hence it becomes $x^2+16x+64$ Factored form- $x^2+16x+64$ $=x^2+8x+8x+64$ $=x(x+8)+8(x+8)$ (Taking the common factors) $=(x+8)(x+8)$ ( $x+8$ is taken common from both the terms) $=(x+8)^2$
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