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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 10: Q 279 (page 1236)

Solve the quadratic equation by quadratic formula . $\frac{1}{8} p^{2} - \frac{1}{5} p = - \frac{1}{20}$

Short Answer

Expert verified

The required result is $p = \frac{4 - \sqrt{6}}{5}, \frac{4 + \sqrt{6}}{5}$

Step by step solution

01

Given Information

The given equation is $\frac{1}{8} p^{2} - \frac{1}{5} p = - \frac{1}{20}$

02

Simplify the expression `to write in standard form

Take LCM

\frac{1}{8} p^{2} - \frac{1}{5} p = - \frac{1}{20} \frac{5 p^{2} - 8 p}{40} = - \frac{1}{20}

$\frac{5 p^{2} - 8 p}{2} = - \frac{1}{1} 5 p^{2} - 8 p = - 2$

$5 p^{2} - 8 p + 2 = 0$

03

After converting in standard form .Identify the value of a,b,c

$a = 5, b = - 8, c = 2$

04

Substitute the values in quadratic formula.

$x = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a} p = \frac{- (- 8) 卤 \sqrt{{(- 8)}^{2} - 4 (5) (2)}}{2 (5)} p = \frac{8 卤 \sqrt{64 - 40}}{10} p = \frac{8 卤 \sqrt{24}}{10} p = \frac{8 卤 2 \sqrt{6}}{10} p = \frac{4 卤 \sqrt{6}}{5} p = \frac{4 - \sqrt{6}}{5}, \frac{4 + \sqrt{6}}{5}$

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