Chapter 9: Q. 9.39 TI (page 884)

Solve by completing the square :
$4 x^{2} + 3 x = 2$

Short Answer

Expert verified

The required value of $x$ is $\frac{- 3 + \sqrt{41}}{8}, \frac{- 3 - \sqrt{41}}{8}$

Step by step solution

Given information

$4 x^{2} + 3 x = 2$

Calculation

$4 x^{2} + 3 x = 2 \Rightarrow \frac{4 x^{2} + 3 x}{4} = \frac{2}{4} \Rightarrow x^{2} + \frac{3}{4} x = \frac{1}{2} \Rightarrow x^{2} + \frac{3}{4} x + {(\frac{1}{2} \times \frac{3}{4})}^{2} = \frac{1}{2} \Rightarrow x^{2} + \frac{3}{4} x + \frac{9}{64} = \frac{1}{2} + \frac{9}{64} \Rightarrow {(x + \frac{3}{8})}^{2} = \frac{41}{64} \Rightarrow x + \frac{3}{8} = \pm \sqrt{\frac{41}{64}} \Rightarrow x = - \frac{3}{8} \pm \frac{\sqrt{41}}{8} = \frac{- 3 + \sqrt{41}}{8}, \frac{- 3 - \sqrt{41}}{8}$

The required value of $x$ is $\frac{- 3 + \sqrt{41}}{8}, \frac{- 3 - \sqrt{41}}{8}$

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 by completing the square :
$4 x^{2} + 3 x = 2$

Short Answer

Step by step solution

Given information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Statistics

Discrete Mathematics

Decision Maths

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve by completing the square :4x2+3x=2

Short Answer

Step by step solution

Given information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Statistics

Discrete Mathematics

Decision Maths

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve by completing the square :
$4 x^{2} + 3 x = 2$