Chapter 9: Q.432. (page 983)

Solve by completing the square.
$4 d^{2} - 2 d = 8$

Short Answer

Expert verified

The solution is $d = \pm \frac{\sqrt{33}}{4} + \frac{1}{4}$ .

Step by step solution

Step 1. Given information.

The given equation is $4 d^{2} - 2 d = 8$ .

Step 2. Simplify the equation.

$\begin{array}{rcl} 4 d^{2} - 2 d & = & 8 \\ \frac{4 d^{2}}{4} - \frac{2 d}{4} & = & \frac{8}{4} \\ d^{2} - \frac{d}{2} & = & 2 \\ d^{2} - 2 \cdot d \cdot \frac{1}{4} & = & 2 \\ d^{2} - 2 \cdot d \cdot \frac{1}{4} + {(\frac{1}{4})}^{2} & = & 2 + {(\frac{1}{4})}^{2} \dots \dots (a d d {(\frac{1}{4})}^{2} o n b o t h s i d e s) \\ {(d - \frac{1}{4})}^{2} & = & 2 + \frac{1}{16} \\ {(d - \frac{1}{4})}^{2} & = & \frac{32 + 1}{16} \\ {(d - \frac{1}{4})}^{2} & = & \frac{33}{16} \end{array}$

Step 3. Solve the equation for d.

$\begin{array}{rcl} {(d - \frac{1}{4})}^{2} & = & \frac{33}{16} \\ d - \frac{1}{4} & = & \pm \sqrt{\frac{33}{16}} \\ d - \frac{1}{4} & = & \pm \frac{\sqrt{33}}{4} \\ d & = & \pm \frac{\sqrt{33}}{4} + \frac{1}{4} \end{array}$

Step 4. Simplified answer.

Hence, the required solution is $d = \pm \frac{\sqrt{33}}{4} + \frac{1}{4}$ .

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.
$4 d^{2} - 2 d = 8$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation.

Step 3. Solve the equation for d.

Step 4. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Logic and Functions

Applied Mathematics

Pure Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve by completing the square.4d2-2d=8

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation.

Step 3. Solve the equation for d.

Step 4. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Logic and Functions

Applied Mathematics

Pure Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve by completing the square.
$4 d^{2} - 2 d = 8$