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: 97

Answer

b = 8 or b = -8

Work Step by Step

In a perfect square trinomial, in th form $ax^{2} + bx + c$, the constant (c) is equal to the square of half the coefficient of the second term, b. $c = (\frac{b}{2})^{2}$ Substitute c with 16 and solve for b. $16 = (\frac{b}{2})^{2}$ To undo the square, we need to take the square root of 16, which will equal to either positive 4 or negative 4. In this case, we will split this off into two equations to solve for the two possible values for the second term coefficient. $4 = \frac{b}{2} $ and $ -4 = \frac{b}{2}$ Solve for b by multiplying both sides of the equation by 2. b = 8 and b = -8
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