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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.409. (page 982)

Solve using the square root property.
$n^{2} + 10 n + 25 = 12$

Short Answer

Expert verified

The solution is $n = 卤 2 \sqrt{3} - 5$ .

Step by step solution

01

Step 1. Given information.

The given equation is $n^{2} + 10 n + 25 = 12$ .

02

Step 2. Apply the square root property.

The property states that if $x = k^{2}$ , then $x = 卤 \sqrt{k}$ .

03

Step 3. Simplify the equation.

$n^{2} + 10 n + 25 = 12 n^{2} + 2 路 n 路 5 + 5^{2} = 12 {(n + 5)}^{2} = 12 n + 5 = 卤 \sqrt{12} n + 5 = 卤 2 \sqrt{3} n = 卤 2 \sqrt{3} - 5$

04

Step 4. Simplified answer.

Hence, the required solution is $n = 卤 2 \sqrt{3} - 5$ .

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