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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. 104 E (page 885)

In the following exercises, solve by completing the square.
$3 d^{2} - 4 d = 15$

Short Answer

Expert verified

The solution is $d = - \frac{5}{3}, d = 3$

Step by step solution

01

Step 1. Given information

Equation: $3 d^{2} - 4 d = 15$

02

Step 2. Calculation

We have,

$3 d^{2} - 4 d = 15$

$\frac{3 d^{2} - 4 d}{3} = \frac{15}{3}$

$d^{2} - \frac{4 d}{3} = 5$

$d^{2} - \frac{4 d}{3} + {(\frac{1}{2} 路 (- \frac{4}{3}))}^{2} = 5 + {(\frac{1}{2} 路 (- \frac{4}{3}))}^{2}$

$d^{2} - \frac{4 d}{3} + {(- \frac{2}{3})}^{2} = 5 + {(- \frac{2}{3})}^{2}$

$d^{2} - \frac{4 d}{3} + \frac{4}{9} = 5 + \frac{4}{9}$

${(d - \frac{2}{3})}^{2} = \frac{49}{9}$

$\sqrt{{(d - \frac{2}{3})}^{2}} = \sqrt{\frac{49}{9}}$

$d - \frac{2}{3} = 卤 \frac{7}{3}$

$d - \frac{2}{3} + \frac{2}{3} = - \frac{7}{3} + \frac{2}{3}, d - \frac{2}{3} + \frac{2}{3} = \frac{7}{3} + \frac{2}{3}$

$d = - \frac{5}{3}, d = \frac{9}{3}$

$d = - \frac{5}{3}, d = 3$

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