Chapter 9: Q36. (page 594)

Solve each equation by completing the square. Round to the nearest tenth if necessary.
$- 3 x^{2} + 4 = 0$

Short Answer

Expert verified

Thesolutions of the quadratic equations are $- 1 .2 and 1 .2$ .

Step by step solution

Step 1. Complete the square.

Complete the square to solve the quadratic equations by isolating andbx-terms.

$- 3 x^{2} + 4 = 0 - 3 x^{2} + 4 - 4 = 0 - 4 [ subtract 4 from each side ] - 3 x^{2} = - 4 3 x^{2} = 4$

Step 2. Take the square root of each side.

Now take the square root of each side.

$\begin{matrix} \sqrt{3 x^{2}} = \sqrt{4} \\ \sqrt{3} x = \pm 2 \end{matrix}$

Step 3. Write the solutions.

Now divide both sides by $\sqrt{3}$ and separate the solutions.

$\sqrt{3} x = \pm 2 \frac{\sqrt{3} x}{\sqrt{3}} = \pm \frac{2}{\sqrt{3}} x = \frac{2}{\sqrt{3}} or x = - \frac{2}{\sqrt{3}}$

Therefore, the solutions are $\frac{2}{\sqrt{3}}$ and $- \frac{2}{\sqrt{3}}$ which is equivalent to respectively.

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.

Solve each equation by completing the square. Round to the nearest tenth if necessary.
$- 3 x^{2} + 4 = 0$

Short Answer

Step by step solution

Step 1. Complete the square.

Step 2. Take the square root of each side.

Step 3. Write the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Discrete Mathematics

Geometry

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Solve each equation by completing the square. Round to the nearest tenth if necessary.−3x2+4=0

Short Answer

Step by step solution

Step 1. Complete the square.

Step 2. Take the square root of each side.

Step 3. Write the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Discrete Mathematics

Geometry

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Solve each equation by completing the square. Round to the nearest tenth if necessary.
$- 3 x^{2} + 4 = 0$