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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. 138 (page 898)

In the following exercises, solve by using the Quadratic Formula.
$\frac{1}{3} n^{2} + n = - \frac{1}{2}$

Short Answer

Expert verified

The solutions of the given equation are $n = - \frac{3}{2} 卤 \frac{\sqrt{3}}{2}$ .

Step by step solution

01

Step 1. Write the quadratic equation in standard form.

The given equation is:

$\frac{1}{3} n^{2} + n = - \frac{1}{2}$

The given equation can be written as:

$\begin{array}{rcl} \frac{1}{3} n^{2} + n + \frac{1}{2} & = & 0 \\ \frac{2 n^{2} + 6 n + 3}{6} & = & 0 \\ 2 n^{2} + 6 n + 3 & = & 0 \end{array}$

02

Step 2. Substitute the values in Quadratic Formula.

Quadratic Formula for the equation $a x^{2} + b x + c = 0$ is:

$x = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$

In the given equation, $a = 2, b = 6, c = 3$ . Substitute these values in Quadratic Formula.

$n = \frac{- 6 卤 \sqrt{(6)^{2} - 4 (2) (3)}}{2 (2)}$

03

Step 3. Simplify the value.

On simplification, we get

$\begin{array}{rcl} n & = & \frac{- 6 卤 \sqrt{36 - 24}}{4} \\ n & = & \frac{- 6 卤 \sqrt{12}}{4} \\ n & = & \frac{- 6}{4} 卤 \frac{2 \sqrt{3}}{4} \\ n & = & - \frac{3}{2} 卤 \frac{\sqrt{3}}{2} \end{array}$

04

Step 4. Conclusion.

The solutions of the given equation are $n = - \frac{3}{2} 卤 \frac{\sqrt{3}}{2}$ .

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Most popular questions from this chapter

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