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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 10.68 (page 1190)

Solve the equation using quadratic formula.
$\frac{1}{9} d^{2} - \frac{1}{2} d = - \frac{1}{2}$

Short Answer

Expert verified

The roots are $d = \frac{3}{2}, d = 3$ .

Step by step solution

01

Given Information.

The given equation is $\frac{1}{9} d^{2} - \frac{1}{2} d = - \frac{1}{2}$ .

02

Write the quadratic equation in standard form and identify a,b,c.

$\frac{1}{9} d^{2} - \frac{1}{2} d = - \frac{1}{2}$

The LCD is $18$ .

Multiply both sides by $18$ .

$18 (\frac{1}{9} d^{2} - \frac{1}{2} d) = - \frac{1}{2} 脳 18 2 d^{2} - 9 d = - 9$

Rewrite in standard form.

$2 d^{2} - 9 d + 9 = 0$

Here,

$a = 2, b = - 9, c = 9$

03

Substitute the values in quadratic formula.

$d = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a} d = \frac{- (- 9) 卤 \sqrt{(- 9)^{2} - 4 (2) (9)}}{2 (2)} d = \frac{9 卤 \sqrt{81 - 72}}{4} d = \frac{9 卤 \sqrt{9}}{4}$

04

Use square root property.

$d = \frac{9 卤 3}{4}$

Rewrite to show two solutions.

$d_{1} = \frac{9 + 3}{4} d_{1} = \frac{12}{4} d_{1} = 3$

and

$d_{2} = \frac{9 - 3}{4} d_{2} = \frac{6}{4} d_{2} = \frac{3}{2}$

Thus, the roots are $d = \frac{3}{2}, d = 3$ .

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