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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. 108 E (page 885)

In the following exercises, solve by completing the square.
$3 q^{2} - 5 q = 9$

Short Answer

Expert verified

The solution is $q = - \frac{\sqrt{133}}{6} + \frac{5}{6}, q = \frac{\sqrt{133}}{6} + \frac{5}{6}$

Step by step solution

01

Step 1. Given information

Equation: $3 q^{2} - 5 q = 9$

02

Step 2. Calculation

We have,

$3 q^{2} - 5 q = 9$

$\frac{3 q^{2} - 5 q}{3} = \frac{9}{3}$

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

role="math" localid="1645180355962" $q^{2} - \frac{5 q}{3} + \frac{25}{36} = 3 + \frac{25}{36}$

role="math" localid="1645180450868" ${(q - \frac{5}{6})}^{2} = \frac{133}{36}$

$\sqrt{{(q - \frac{5}{6})}^{2}} = \sqrt{\frac{133}{36}}$

$q - \frac{5}{6} = 卤 \frac{\sqrt{133}}{6}$

$q - \frac{5}{6} + \frac{5}{6} = - \frac{\sqrt{133}}{6} + \frac{5}{6}, q - \frac{5}{6} + \frac{5}{6} = \frac{\sqrt{133}}{6} + \frac{5}{6}$

$q = - \frac{\sqrt{133}}{6} + \frac{5}{6}, q = \frac{\sqrt{133}}{6} + \frac{5}{6}$

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