Chapter 10: Q 223. (page 1235)

In the following exercises, solve using the Square Root Property.
$5 c^{2} + 3 = 19$

Short Answer

Expert verified

The required answer is $c = \frac{4 \sqrt{5}}{5} and c = - \frac{4 \sqrt{5}}{5}$ .

Step by step solution

Step 1. Given information.

The given quadratic equation is:

$5 c^{2} + 3 = 19$

Step 2. Solve using the quadratic equation by using Square Root Property.

$5 c^{2} + 3 = 19$

Isolate the quadratic term and make its coefficient one by subtracting 3 from both sides,

$5 c^{2} + 3 - 3 = 19 - 3 5 c^{2} = 16$

Divide both sides by 5,

localid="1653448355102" $\frac{5 c^{2}}{5} = \frac{16}{5} c^{2} = \frac{16}{5}$

Use Square Root Property,

$c = \pm \sqrt{\frac{16}{5}}$

Simplify the radical,

localid="1653448459356" $c = \pm \frac{\sqrt{16}}{\sqrt{5}} c = \pm \frac{4}{\sqrt{5}} c = \pm \frac{4 \sqrt{5}}{5}$

Rewrite to show two solutions,

localid="1653448429279" $c = \frac{4 \sqrt{5}}{5} a n d c = - \frac{4 \sqrt{5}}{5}$

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 using the Square Root Property.
$5 c^{2} + 3 = 19$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve using the quadratic equation by using Square Root Property.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Logic and Functions

Discrete Mathematics

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve using the Square Root Property.5c2+3=19

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve using the quadratic equation by using Square Root Property.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Logic and Functions

Discrete Mathematics

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve using the Square Root Property.
$5 c^{2} + 3 = 19$