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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.441. (page 983)

Solve by using the quadratic formula.
$3 m^{2} + 8 m + 2 = 0$

Short Answer

Expert verified

The solution is $m = \frac{- 4 卤 \sqrt{10}}{3}$ .

Step by step solution

01

Step 1. Given information.

The given equation is $3 m^{2} + 8 m + 2 = 0$ .

02

Step 2. Write the equation in standard form.

The standard form of the quadratic equation is $a m^{2} + b m + c = 0$ .

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

So, here $a = 3, b = 8, c = 2$ .

03

Step 3. Apply the quadratic formula.

The quadratic formula is $m = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$ .

Substitute $a = 3, b = 8, c = 2$ in the above result.

$\begin{array}{rcl} m & = & \frac{- 8 卤 \sqrt{8^{2} - 4 脳 3 脳 2}}{2 脳 3} \\ = & \frac{- 8 卤 \sqrt{64 - 24}}{6} \\ = & \frac{- 8 卤 \sqrt{40}}{6} \\ = & \frac{- 8 卤 2 \sqrt{10}}{6} \\ = & \frac{2 (- 4 卤 \sqrt{10})}{2 脳 3} \\ = & \frac{- 4 卤 \sqrt{10}}{3} \end{array}$

04

Step 4. Simplified answer.

Hence, the required solution is $m = \frac{- 4 卤 \sqrt{10}}{3}$ .

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