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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.448. (page 983)

Solve by using the quadratic formula.
$\frac{2}{5} q^{2} + \frac{3}{10} q = \frac{1}{10}$

Short Answer

Expert verified

The solution is $q = \frac{1}{4}$ and $q = - 1$ .

Step by step solution

01

Step 1. Given information.

The given equation is $\frac{2}{5} q^{2} + \frac{3}{10} q = \frac{1}{10}$ .

02

Step 2. Write the equation in standard form.

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

The LCM of $(5, 10, 10)$ is $10$ .

So, multiply both sides of the equation by LCM $10$ .

$\begin{array}{rcl} 10 脳 \frac{2}{5} q^{2} + 10 脳 \frac{3}{10} q & = & \frac{1}{10} 脳 10 \\ 4 q^{2} + 3 q & = & 1 \\ 4 q^{2} + 3 q + (- 1) & = & 0 \end{array}$

So, here $a = 4, b = 3, c = - 1$ .

03

Step 3. Apply the quadratic formula.

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

$\begin{array}{rcl} q & = & \frac{- 3 卤 \sqrt{3^{2} - 4 脳 4 脳 (- 1)}}{2 脳 4} 鈰� 鈰� (a = 4, b = 3, c = - 1) \\ = & \frac{- 3 卤 \sqrt{9 + 16}}{8} \\ = & \frac{- 3 卤 \sqrt{25}}{8} \\ = & \frac{- 3 卤 5}{8} \end{array}$

04

Step 4. Solve the equation for q.

$\begin{array}{rcl} q & = & \frac{- 3 + 5}{8} \\ = & \frac{2}{8} \\ = & \frac{1}{4} \end{array}$ and $\begin{array}{rcl} q & = & \frac{- 3 - 5}{8} \\ = & \frac{- 8}{8} \\ = & - 1 \end{array}$

05

Step 5. Simplified answer.

Hence, the required solution is $q = \frac{1}{4}$ and $q = - 1$ .

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