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 - Page 764: 30



Work Step by Step

We add the square of half of the coefficent of $x$ so that the result is a perfect square trinomial. Co-efficient of $x=-8$ Half of -8 is $\frac{1}{2}×-8=-4$ Square of -4 is $-4×-4=16$ We add 16 to $x^2-8x$ to make it a perfect square trinomial. Hence it becomes $x^2-8x+16$ Factored form- $x^2-8x+16$ $=x^2-4x-4x+16$ $=x(x-4)-4(x-4)$ (Taking the common factors) $=(x-4)(x-4)$ ($ x-4$ is taken common from both the terms) $=(x-4)^2$
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