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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. 137 (page 898)

In the following exercises, solve by using the Quadratic Formula.
$\frac{1}{3} m^{2} + \frac{1}{12} m = \frac{1}{4}$

Short Answer

Expert verified

The solutions of the given equation are $m = - 1$ and $m = \frac{3}{4}$ .

Step by step solution

01

Step 1. Write the quadratic equation in standard form.

The given equation is:

$\frac{1}{3} m^{2} + \frac{1}{12} m = \frac{1}{4}$

The given equation can be written as:

$\begin{array}{rcl} \frac{1}{3} m^{2} + \frac{1}{12} m - \frac{1}{4} & = & 0 \\ \frac{4 m^{2} + m - 3}{12} & = & 0 \\ 4 m^{2} + m - 3 & = & 0 \end{array}$

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, $a = 4, b = 1, c = - 3$ . Substitute these values in Quadratic Formula.

$m = \frac{- 1 卤 \sqrt{(1)^{2} - 4 (4) (- 3)}}{2 (4)}$

03

Step 3. Simplify the value.

On simplification, we get

$\begin{array}{rcl} m & = & \frac{- 1 卤 \sqrt{1 + 48}}{8} \\ m & = & \frac{- 1 卤 \sqrt{49}}{8} \\ m & = & \frac{- 1 卤 7}{8} \end{array}$

It can be written as:

$\begin{array}{rcl} m & = & \frac{- 1 + 7}{8} and m = \frac{- 1 - 7}{8} \\ m & = & \frac{6}{8} and m = \frac{- 8}{8} \\ m & = & \frac{3}{4} and m = - 1 \end{array}$

04

Step 4. Conclusion.

The solutions of the given equation are $m = - 1$ and $m = \frac{3}{4}$ .

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