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: 5

Answer

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

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 $x = 12$ Half of 12 is $\frac{1}{2} \times 12= 6 $ Square of 6 is $6\times6=36$ We add 36 to $x^2+12x$ to make it a perfect square trinomial. Hence it becomes $x^2+12x + 36$ Factored form- $x^2+12x + 36$ $= x^2+6x+ 6x + 36$ $= x(x + 6) + 6(x+6)$ (Taking the common factors) $= (x+6) (x+6)$ ( x+6 is taken common from both the terms) $=(x+6)^2$
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