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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 327. (page 1240)

Solve the quadratic equations below. Use any method you want.
$3 n^{2} + 8 n + 3 = 0$

Short Answer

Expert verified

As a result, the two solutions are $n = \frac{- 4 - \sqrt{7}}{3}$ and $n = \frac{- 4 + \sqrt{7}}{3}$ .

Step by step solution

01

Given information.

The given equation is

$3 n^{2} + 8 n + 3 = 0$

02

Step 2. Use the quadratic formula to solve the equation.

First, write the equation $a x^{2} + b x + c = 0$ in standard form, as shown below.

This is already done in this place.

Determine the a, b, and c values.

When compared to the standard, the values are a = 3 b = 8 and c= 3.

In the quadratic formula, substitute a=3,b=8, and c= 3.

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

role="math" localid="1653847814613" $n = \frac{8 卤 \sqrt{{(8)}^{2} - 4 (3) (3)}}{2 (3)}$

As shown below, simplify the fraction.

$n = \frac{- 8 卤 \sqrt{{(8)}^{2} - 4 (3) (3)}}{2 (3)} n = \frac{- 8 卤 \sqrt{64 - 36}}{6} n = \frac{- 8 卤 \sqrt{28}}{6} \frac{n = - 4 卤 2 \sqrt{7}}{3}$

As a result, the two solutions are $n = \frac{- 4 - \sqrt{7}}{3}$ and $\frac{n = - 4 + \sqrt{7}}{3}$ .

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