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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. 92 E (page 885)

Solve quadratic equations of the form $x^{2} + b x + c = 0$ by completing the square.
In the following exercises , solve by completing the square.
$w^{2} = 5 w - 1$

Short Answer

Expert verified

The required value of $w$ is $\frac{5 + \sqrt{21}}{2}, \frac{5 - \sqrt{21}}{2}$

Step by step solution

01

Given information

$w^{2} = 5 w - 1$

02

Calculation

$w^{2} = 5 w - 1 鈬� w^{2} - 5 w = - 1 鈬� w^{2} - 5 w + (\frac{1}{2} 脳 {(- 5))}^{2} = - 1 鈬� w^{2} - 5 w + \frac{25}{4} = - 1 + \frac{25}{4} 鈬� {(w - \frac{5}{2})}^{2} = \frac{21}{4} 鈬� w - \frac{5}{2} = 卤 \sqrt{\frac{21}{4}} = 卤 \frac{\sqrt{21}}{2} 鈬� w = \frac{5}{2} 卤 \frac{\sqrt{21}}{2} = \frac{5 + \sqrt{21}}{2}, \frac{5 - \sqrt{21}}{2}$

The required value of $w$ is $\frac{5 + \sqrt{21}}{2}, \frac{5 - \sqrt{21}}{2}$

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Most popular questions from this chapter

Use the Discriminant to Predict the Number of Solutions of a Quadratic Equation.

In the following exercises, determine the number of solutions for each quadratic equation.

$(a) 9 v^{2} - 15 v + 25 = 0 (b) 100 w^{2} + 60 w + 9 = 0 (c) 5 c^{2} + 7 c - 10 = 0$

It takes two hours for two machines to manufacture 10,000 parts. If Machine #1 can do the job alone in one hour less than Machine #2 can do the job, how long does it take for each machine to manufacture 10,000 parts alone?

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