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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.9.20 (page 868)

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

Short Answer

Expert verified

The solutions of the quadratic equation: $n = - \frac{3}{4}, n = - \frac{7}{4}$ .

Step by step solution

01

Step 1. Given information

Consider the quadratic equation

$16 n^{2} + 40 n + 25$

Factor the perfect square trinomial.

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

Use the Square Root Property.

$4 n + 5 = 卤 \sqrt{4} 4 n + 5 = 卤 2$

Subtract 5 from both sides.

$4 n = 卤 2 - 5$

Solve for $n$ .

$n = \frac{卤 2 - 5}{4}$

Rewrite to show two solutions.

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

02

Step 2. Check for solutions.

Substitute $n = - \frac{3}{4}$ in the original equation.

$16 n^{2} + 40 n + 25 = 4 16 {(- \frac{3}{4})}^{2} + 40 (- \frac{3}{4}) + 25 \overset{?}{=} 4 16 (\frac{9}{16}) - 30 + 25 \overset{?}{=} 4 4 = 4$

Substitute $n = - \frac{7}{4}$ in the original equation.

$16 n^{2} + 40 n + 25 = 4 16 {(- \frac{7}{4})}^{2} + 40 (- \frac{7}{4}) + 25 \overset{?}{=} 4 16 (\frac{49}{16}) - 70 + 25 \overset{?}{=} 4 4 = 4$

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