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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 9.31 (page 879)

Solve by completing the square :
$p^{2} = 5 p + 9$

Short Answer

Expert verified

The required value of $x$ is $\frac{5 + \sqrt{61}}{2}, \frac{5 - \sqrt{61}}{2}$

Step by step solution

01

Given information

$p^{2} = 5 p + 9$

02

Calculation

$p^{2} = 5 p + 9 鈬� p^{2} - 5 p = 9 鈬� p^{2} - 5 p + (\frac{1}{2} 脳 {(- 5))}^{2} = 9 鈬� p^{2} - 5 p + \frac{25}{4} = 9 + \frac{25}{4} 鈬� {(p - \frac{5}{2})}^{2} = \frac{61}{4} 鈬� p - \frac{5}{2} = 卤 \sqrt{\frac{61}{4}} 鈬� p = \frac{5}{2} 卤 \frac{\sqrt{61}}{2} = \frac{5 + \sqrt{61}}{2}, \frac{5 - \sqrt{61}}{2}$

The required value of $x$ is $\frac{5 + \sqrt{61}}{2}, \frac{5 - \sqrt{61}}{2}$

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