Q.431. Solve by completing the square.3... [FREE SOLUTION]

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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.431. (page 983)

Solve by completing the square.
$3 c^{2} + 2 c = 9$

Short Answer

Expert verified

The solution is $c = 卤 \frac{2 \sqrt{7}}{3} - \frac{1}{3}$ .

Step by step solution

Step 1. Given information.

The given equation is $3 c^{2} + 2 c = 9$ .

Step 2. Simplify the given equation.

$\begin{array}{rcl} 3 c^{2} + 2 c & = & 9 \\ \frac{3 c^{2}}{3} + \frac{2 c}{3} & = & \frac{9}{3} \\ c^{2} + \frac{2 c}{3} & = & 3 \\ c^{2} + 2 路 c 路 \frac{1}{3} & = & 3 \\ c^{2} + 2 路 c 路 \frac{1}{3} + {(\frac{1}{3})}^{2} & = & 3 + {(\frac{1}{3})}^{2} \\ {(c + \frac{1}{3})}^{2} & = & 3 + \frac{1}{9} \\ {(c + \frac{1}{3})}^{2} & = & \frac{27 + 1}{9} \\ {(c + \frac{1}{3})}^{2} & = & \frac{28}{9} \end{array}$

Step 3. Solve the above calculation for c.

$\begin{array}{rcl} {(c + \frac{1}{3})}^{2} & = & \frac{28}{9} \\ c + \frac{1}{3} & = & 卤 \sqrt{\frac{28}{9}} \\ c + \frac{1}{3} & = & 卤 \frac{2 \sqrt{7}}{3} \\ c & = & 卤 \frac{2 \sqrt{7}}{3} - \frac{1}{3} \end{array}$

Step 4. Simplified answer.

Hence, the required solution is $\begin{array}{rcl} c & = & 卤 \frac{2 \sqrt{7}}{3} - \frac{1}{3} \end{array}$ .

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91影视

Solve by completing the square.
$3 c^{2} + 2 c = 9$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the given equation.

Step 3. Solve the above calculation for c.

Step 4. Simplified answer.

One App. One Place for Learning.

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91影视

Solve by completing the square.3c2+2c=9

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the given equation.

Step 3. Solve the above calculation for c.

Step 4. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Geometry

Applied Mathematics

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

Solve by completing the square.
$3 c^{2} + 2 c = 9$