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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 10.52 (page 1179)

Solve $4 t^{2} + 2 t = 20$ by completing the square.

Short Answer

Expert verified

The values of $t$ for the equation $4 t^{2} + 2 t = 20$ by completing the squares are $2, - \frac{5}{2}$ .

Step by step solution

01

Step 1. Given Information.

The equation is $4 t^{2} + 2 t = 20$ .

02

Step 2. Using completing the square method.

Given, $4 t^{2} + 2 t = 20$

Dividing both sides by $4$ ,

$鈬� \frac{4 t^{2} + 2 t}{4} = \frac{20}{4} 鈬� t^{2} + \frac{1}{2} t = 5$

Taking the square of the half of $\frac{1}{2}$ and adding it on both sides,

$鈬� t^{2} + \frac{1}{2} t + {(\frac{1}{2} (\frac{1}{2}))}^{2} = 5 + {(\frac{1}{2} (\frac{1}{2}))}^{2} 鈬� t^{2} + \frac{1}{2} t + \frac{1}{16} = 5 + \frac{1}{16} 鈬� t^{2} + \frac{1}{2} t + \frac{1}{16} = \frac{81}{16}$

Factoring the right side as a binomial square,

$鈬� {(t + \frac{1}{4})}^{2} = \frac{81}{16}$

Taking the square root on both sides,

$鈬� t + \frac{1}{4} = \sqrt{\frac{81}{16}} 鈬� t + \frac{1}{4} = 卤 \frac{9}{4}$

Solving for $t$ ,

$鈬� t = - \frac{1}{4} 卤 \frac{9}{4} 鈬� t = - \frac{1}{4} + \frac{9}{4} o r, t = - \frac{1}{4} - \frac{9}{4} 鈬� t = 2, - \frac{5}{2}$

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