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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 280 (page 1236)

Solve the quadratic equation by quadratic formula . $\frac{2}{3} q^{2} + \frac{3}{10} q = \frac{1}{10}$

Short Answer

Expert verified

The required result is $q = \frac{- 9 + \sqrt{321}}{40}, \frac{- 9 - \sqrt{321}}{40}$

Step by step solution

01

Given Information

The given equation is $\frac{2}{3} q^{2} + \frac{3}{10} q = \frac{1}{10}$

02

Simplify the expression `to write in standard form

LCM,

$\frac{20 q^{2} + 9 q}{30} = \frac{1}{10} \frac{20 q^{2} + 9 q}{3} = 1 20 q^{2} + 9 q = 3$

$20 q^{2} + 9 q - 3 = 0$

03

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

$a = 20, b = 9, c = - 3$

04

Substitute the values in quadratic formula.

$x = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$

q = \frac{- (9) 卤 \sqrt{{(9)}^{2} - 4 (20) (- 3)}}{2 (20)} q = \frac{- 9 卤 \sqrt{81 + 240}}{40} q = \frac{- 9 卤 \sqrt{321}}{40}

$q = \frac{- 9 + \sqrt{321}}{40}, \frac{- 9 - \sqrt{321}}{40}$

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