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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 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

$4 n^{2} - 24 n - 56 = 8 \Rightarrow 4 (n^{2} - 6 n - 14) = 8 \Rightarrow \frac{4 (n^{2} - 6 n - 14)}{4} = \frac{8}{4} \Rightarrow n^{2} - 6 n - 14 = 2 \Rightarrow n^{2} - 6 n = 14 + 2 \Rightarrow n^{2} - 6 n + (\frac{1}{2} \times {(- 6))}^{2} = 16 \Rightarrow n^{2} - 6 n + 9 = 16 + 9 \Rightarrow {(n - 3)}^{2} = 25 \Rightarrow n - 3 = \pm \sqrt{25} \Rightarrow n - 3 = \pm 5 \Rightarrow n = 3 \pm 5 = 3 + 5, 3 - 5 = 8, - 2$

The required value of $n$ is

8, - 2

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