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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 10: Q 10.54 (page 1180)

Solve $5 y^{2} + 3 y = 10$ by completing the square.

Short Answer

Expert verified

The value of $y$ for the equation $5 y^{2} + 3 y = 10$ by completing the square are $\frac{- 3 + \sqrt{209}}{10}, \frac{- 3 - \sqrt{209}}{10}$ .

Step by step solution

01

Step 1. Given Information.

The equation is,

$5 y^{2} + 3 y = 10$ .

02

Step 2. Completing the square.

Given, $5 y^{2} + 3 y = 10$ .

Dividing both sides by $5$ to remove the coefficient of $y^{2}$ on both sides,

$鈬� \frac{5 y^{2} + 3 y}{5} = \frac{10}{5} 鈬� y^{2} + \frac{3}{5} y = 2$

Adding the square of half of $\frac{3}{5}$ on both sides,

$鈬� y^{2} + \frac{3}{5} y + {(\frac{1}{2} (\frac{3}{5}))}^{2} = 2 + {(\frac{1}{2} (\frac{3}{5}))}^{2} 鈬� y^{2} + \frac{3}{5} y + \frac{9}{100} = 2 + \frac{9}{100} 鈬� y^{2} + \frac{3}{5} y + \frac{9}{100} = \frac{209}{100}$

Writing the left side as a binomial square,

$鈬� {(y + \frac{3}{10})}^{2} = \frac{209}{100}$

Taking the square root on both sides,

$鈬� y + \frac{3}{10} = \sqrt{\frac{209}{100}} 鈬� y + \frac{3}{10} = 卤 \frac{\sqrt{209}}{10}$

Solving for the value of $y$ , we get,

$鈬� y = - \frac{3}{10} 卤 \frac{\sqrt{209}}{10} 鈬� y = - \frac{3}{10} + \frac{\sqrt{209}}{10} o r, y = - \frac{3}{10} - \frac{\sqrt{209}}{10} 鈬� y = \frac{- 3 + \sqrt{209}}{10}, \frac{- 3 - \sqrt{209}}{10}$

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