Chapter 9: Q. 107 E (page 885)

In the following exercises, solve by completing the square.
$2 p^{2} + 7 p = 14$

Short Answer

Expert verified

The solution is $p = - \frac{\sqrt{161}}{4} - \frac{7}{4}, p = \frac{\sqrt{161}}{4} - \frac{7}{4}$

Step by step solution

Step 1. Given information

Equation: $2 p^{2} + 7 p = 14$

Step 2. Calculation

We have,

$2 p^{2} + 7 p = 14$

$\frac{2 p^{2} + 7 p}{2} = \frac{14}{2}$

$p^{2} + \frac{7 p}{2} + {(\frac{1}{2} \cdot (\frac{7}{2}))}^{2} = 7 + {(\frac{1}{2} \cdot (\frac{7}{2}))}^{2}$

$p^{2} + \frac{7 p}{2} + {(\frac{7}{4})}^{2} = 7 + {(\frac{7}{4})}^{2}$

$p^{2} + \frac{7 p}{2} + \frac{49}{16} = 7 + \frac{49}{16}$

${(p + \frac{7}{4})}^{2} = \frac{161}{16}$

$\sqrt{{(p + \frac{7}{4})}^{2}} = \sqrt{\frac{161}{16}}$

$p + \frac{7}{4} = \pm \frac{\sqrt{161}}{4}$

$p + \frac{7}{4} - \frac{7}{4} = - \frac{\sqrt{161}}{4} - \frac{7}{4}, p + \frac{7}{4} - \frac{7}{4} = \frac{\sqrt{161}}{4} - \frac{7}{4}$

localid="1645180152491" $p = - \frac{\sqrt{161}}{4} - \frac{7}{4}, p = \frac{\sqrt{161}}{4} - \frac{7}{4}$

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.

In the following exercises, solve by completing the square.
$2 p^{2} + 7 p = 14$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Decision Maths

Applied Mathematics

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve by completing the square.2p2+7p=14

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Decision Maths

Applied Mathematics

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve by completing the square.
$2 p^{2} + 7 p = 14$