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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 9.30 (page 1069)

Solve by completing the square :
$b^{2} + 8 b - 4 = 16$

Short Answer

Expert verified

The required value of $x$ is $2, - 10$

Step by step solution

01

Given information

$b^{2} + 8 b - 4 = 16$

02

Calculation

$b^{2} + 8 b - 4 = 16 鈬� b^{2} + 8 b = 16 + 4 鈬� b^{2} + 8 b + {(\frac{1}{2} 脳 8)}^{2} = 20 + 16 鈬� b^{2} + 8 b + 16 = 20 + 16 鈬� {(b + 4)}^{2} = 36 鈬� b + 4 = 卤 \sqrt{36} = 卤 6 鈬� b = - 4 卤 6 = - 4 + 6, - 4 - 6 = 2, - 10$

The required value of $x$ is $- 10, 2$

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Most popular questions from this chapter

In the following exercise, factor using substitution.

${(x 鈭� 3)}^{2} 鈭� 5 (x 鈭� 3) 鈭� 36$

In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .

$a^{2} + 14 a + 33$

In the following exercises, factor each expression using any method $6 r^{2} + 30 r + 36$

Factor $u^{2} - 9 u + 18$

Simplify:

(a) ${(- 256)}^{\frac{1}{4}}$

(b) ${- 256}^{\frac{1}{4}}$

(c) ${(256)}^{- \frac{1}{4}}$

See all solutions

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