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: 29

Answer

$z^2-12z+36=(x-6)^2$

Work Step by Step

We add the square of half of the coefficent of $z$ so that the result is a perfect square trinomial. Co-efficient of $z=-12$ Half of -12 is $\frac{1}{2}×-12=-6$ Square of -6 is $-6×-6=36$ We add 36 to $z^2-12z$ to make it a perfect square trinomial. Hence it becomes $z^2-12z+36$ Factored form- $z^2-12z+36$ $=z^2-6z-6z+36$ $=z(z-6)-6(z-6)$ (Taking the common factors) $=(z-6)(z-6)$ ($ z-6$ is taken common from both the terms) $=(z-6)^2$
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