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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 9.36 TI (page 881)

Solve by completing the square :
$4 n^{2} - 24 n - 56 = 8$

Short Answer

Expert verified

The required value of $n$ is $8, - 2$

Step by step solution

01

Given information

$4 n^{2} - 24 n - 56 = 8$

02

Calculation

$4 n^{2} - 24 n - 56 = 8 鈬� 4 (n^{2} - 6 n - 14) = 8 鈬� \frac{4 (n^{2} - 6 n - 14)}{4} = \frac{8}{4} 鈬� n^{2} - 6 n - 14 = 2 鈬� n^{2} - 6 n = 14 + 2 鈬� n^{2} - 6 n + (\frac{1}{2} 脳 {(- 6))}^{2} = 16 鈬� n^{2} - 6 n + 9 = 16 + 9 鈬� {(n - 3)}^{2} = 25 鈬� n - 3 = 卤 \sqrt{25} 鈬� n - 3 = 卤 5 鈬� n = 3 卤 5 = 3 + 5, 3 - 5 = 8, - 2$

The required value of $n$ is

8, - 2

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