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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 9.37 TI (page 1069)

Solve by completing the square :
$3 r^{2} - 2 r = 21$

Short Answer

Expert verified

The required value of $r$ is $3, \frac{- 7}{3}$

Step by step solution

01

Given information

$3 r^{2} - 2 r = 21$

02

Calculation

$3 r^{2} - 2 r = 21 鈬� \frac{3 r^{2} - 2 r}{3} = \frac{21}{3} + \frac{1}{9} 鈬� r^{2} - \frac{2}{3} r = 7 鈬� r^{2} - \frac{2}{3} r + (\frac{1}{2} 脳 {(- \frac{2}{3}))}^{2} = 7 鈬� r^{2} - \frac{2}{3} r + \frac{1}{9} = 7 + \frac{1}{9} 鈬� {(r - \frac{1}{3})}^{2} = \frac{64}{9} 鈬� r - \frac{1}{3} = 卤 \sqrt{\frac{64}{9}} 鈬� r = \frac{1}{3} 卤 \sqrt{\frac{64}{9}} = \frac{1}{3} 卤 \frac{8}{3} = \frac{1 + 8}{3}, \frac{1 - 8}{3} = \frac{9}{3}, \frac{- 7}{3} = 3, \frac{- 7}{3}$

The required value of $r$ is $3, \frac{- 7}{3}$

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Most popular questions from this chapter

In the following exercises, divide the rational expressions.

$\frac{p^{3} + q^{3}}{3 p^{2} + 3 p q + 3 q^{2}} 梅 \frac{p^{2} - q^{2}}{12}$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{n^{21}}, \sqrt[3]{q^{8}}, \sqrt[8]{n^{10}}$

In the following exercises, factor.

$鈭� 4 x^{3} y^{5} 鈭� x^{2} y^{3} + 12 x y^{4}$ .

In the following exercises, simplify using absolute value signs as needed.

$a . 8 + \sqrt{96} b . \frac{8 鈭� \sqrt{80}}{4}$

Explain why an equation of the form $\sqrt{x} + 1 = 0$ has no solution.

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