Chapter 9: Q. 140 (page 898)

In the following exercises, solve by using the Quadratic Formula.
$\frac{1}{9} c^{2} + \frac{2}{3} c = 3$

Short Answer

Expert verified

The solutions of the given equation are $b = 3$ and $b = - 9$ .

Step by step solution

Step 1. Write the quadratic equation in standard form.

The given equation is:

$\frac{1}{9} c^{2} + \frac{2}{3} c = 3$

The given equation can be written as:

$\begin{array}{rcl} \frac{1}{9} c^{2} + \frac{2}{3} c - 3 & = & 0 \\ \frac{c^{2} + 6 c - 27}{9} & = & 0 \\ c^{2} + 6 c - 27 & = & 0 \end{array}$

Step 2. Substitute the values in Quadratic Formula.

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

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

In the given equation, $a = 1, b = 6, c = - 27$ . Substitute these values in Quadratic Formula.

$b = \frac{- 6 \pm \sqrt{(6)^{2} - 4 (1) (- 27)}}{2 (1)}$

Step 3. Simplify the value.

On simplification, we get

$\begin{array}{rcl} b & = & \frac{- 6 \pm \sqrt{36 + 108}}{2} \\ b & = & \frac{- 6 \pm \sqrt{144}}{2} \\ b & = & \frac{- 6}{2} \pm \frac{12}{2} \\ b & = & - 3 \pm 6 \end{array}$

It can be wriitten as:

$\begin{array}{rcl} b & = & - 3 + 6 and b = - 3 - 6 \\ b & = & 3 and b = - 9 \end{array}$

Step 4. Conclusion.

The solutions of the given equation are $b = 3$ and $b = - 9$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, solve by using the Quadratic Formula.
$\frac{1}{9} c^{2} + \frac{2}{3} c = 3$

Short Answer

Step by step solution

Step 1. Write the quadratic equation in standard form.

Step 2. Substitute the values in Quadratic Formula.

Step 3. Simplify the value.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Logic and Functions

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve by using the Quadratic Formula.19c2+23c=3

Short Answer

Step by step solution

Step 1. Write the quadratic equation in standard form.

Step 2. Substitute the values in Quadratic Formula.

Step 3. Simplify the value.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Logic and Functions

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve by using the Quadratic Formula.
$\frac{1}{9} c^{2} + \frac{2}{3} c = 3$