Chapter 10: Q 93 (page 1181)

Solve by completing the square:
$2 p^{2} + 7 p = 14$ .

Short Answer

Expert verified

The value of $p$ for the equation $2 p^{2} + 7 p = 14$ by completing the square are $\frac{\sqrt{161} - 7}{4}, \frac{- \sqrt{161} - 7}{4}$ .

Step by step solution

Step 1. Given Information.

The equation is,

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

Step 2. Completing the square.

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

Dividing both sides by $2$ to eliminate the coefficient of $p^{2}$ ,

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

Adding the square of half of $\frac{7}{2}$ on both the sides,

$\Rightarrow p^{2} + \frac{7}{2} p + {(\frac{1}{2} (\frac{7}{2}))}^{2} = 7 + {(\frac{1}{2} (\frac{7}{2}))}^{2} \Rightarrow p^{2} + \frac{7}{2} p + \frac{49}{16} = 7 + \frac{49}{16} \Rightarrow p^{2} + \frac{7}{2} p + \frac{49}{16} = \frac{161}{16}$

Writing the Left Hand Side as a binomial square.

role="math" localid="1653672948257" $\Rightarrow {(p + \frac{7}{4})}^{2} = \frac{161}{16}$

Taking the square root on both sides,

$\Rightarrow p + \frac{7}{4} = \sqrt{\frac{161}{16}} \Rightarrow p + \frac{7}{4} = \pm \frac{\sqrt{161}}{4}$

Solving for the value of $p$ ,

$\Rightarrow p = \pm \frac{\sqrt{161}}{4} - \frac{7}{4} \Rightarrow p = \frac{\sqrt{161} - 7}{4} o r, p = \frac{- \sqrt{161} - 7}{4} \Rightarrow p = \frac{\sqrt{161} - 7}{4}, \frac{- \sqrt{161} - 7}{4}$

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Solve by completing the square:
$2 p^{2} + 7 p = 14$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Completing the square.

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Solve by completing the square:2p2+7p=14.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Completing the square.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Decision Maths

Probability and Statistics

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve by completing the square:
$2 p^{2} + 7 p = 14$ .