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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 10: Q 10.26 (page 1164)

Solve $16 n^{2} + 40 n + 25 = 4$ .

Short Answer

Expert verified

The solutions are $n = \frac{- 7}{4}, \frac{- 3}{4}$ .

Step by step solution

01

Given Information.

The Given equation is $16 n^{2} + 40 n + 25 = 4$ .

02

Factor the trinomial.

$(4 n)^{2} + (2 脳 5 脳 4) + (5)^{2} = 4 (4 n + 5)^{2} = 4$

Use square root property.

$4 n + 5 = 卤 \sqrt{4} 4 n + 5 = 卤 2$

03

Isolate the term.

$n = \frac{- 5 卤 2}{4}$

Rewrite to show two solutions.

$n = \frac{- 5 + 2}{4} = \frac{- 3}{4} n = \frac{- 5 - 2}{4} = \frac{- 7}{4}$

The solutions are $n = \frac{- 7}{4}, \frac{- 3}{4}$ .

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