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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. 109 E (page 885)

In the following exercises, solve by completing the square.
$5 x^{2} - 3 x = - 10$

Short Answer

Expert verified

The solution is $x = \frac{3}{10} - \frac{\sqrt{191} i}{10}, x = \frac{3}{10} + \frac{\sqrt{191} i}{10}$

Step by step solution

01

Step 1. Given information

Equation: $5 x^{2} - 3 x = - 10$

02

Step 2. Calculation

We have,

$5 x^{2} - 3 x = - 10$

$\frac{5 x^{2} - 3 x}{5} = \frac{- 10}{5}$

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

role="math" localid="1645182571593" $x^{2} - \frac{3 x}{5} + \frac{9}{100} = - 2 + \frac{9}{100}$

role="math" localid="1645182680652" ${(x - \frac{3}{10})}^{2} = - \frac{191}{100}$

role="math" localid="1645182688837" $\sqrt{{(x - \frac{3}{10})}^{2}} = \sqrt{- \frac{191}{100}}$

$x - \frac{3}{10} = 卤 \frac{\sqrt{191} i}{10}$

$x - \frac{3}{10} + \frac{3}{10} = \frac{3}{10} - \frac{\sqrt{191} i}{10}, x - \frac{3}{10} + \frac{3}{10} = \frac{3}{10} + \frac{\sqrt{191} i}{10}$

$x = \frac{3}{10} - \frac{\sqrt{191} i}{10}, x = \frac{3}{10} + \frac{\sqrt{191} i}{10}$

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