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

Given Information.

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

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 $18$ .

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

Rewrite in standard form.

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

Here,

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

Substitute the values in quadratic formula.

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

Use square root property.

$d = \frac{9 \pm 3}{4}$

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 $d = \frac{3}{2}, d = 3$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Short Answer

Step by step solution

Given Information.

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

Substitute the values in quadratic formula.

Use square root property.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Theoretical and Mathematical Physics

Probability and Statistics

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve the equation using quadratic formula. 19d2-12d=-12

Short Answer

Step by step solution

Given Information.

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

Substitute the values in quadratic formula.

Use square root property.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Theoretical and Mathematical Physics

Probability and Statistics

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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