Chapter 9: Q. 9.38 TI (page 882)

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

Short Answer

Expert verified

The required value of $t$ is $2, \frac{- 5}{2}$

Step by step solution

Given information

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

Calculation

$4 t^{2} + 2 t = 20 \Rightarrow \frac{4 t^{2} + 2 t}{4} = \frac{20}{4} \Rightarrow t^{2} + \frac{1}{2} t = 5 \Rightarrow t^{2} + 2 t + {(\frac{1}{2} \times \frac{1}{2})}^{2} = 5 \Rightarrow t^{2} + 2 t + \frac{1}{16} = 5 + \frac{1}{16} \Rightarrow {(t + \frac{1}{4})}^{2} = \frac{81}{16} \Rightarrow t + \frac{1}{4} = \pm \sqrt{\frac{81}{16}} \Rightarrow t = - \frac{1}{4} \pm \sqrt{\frac{81}{16}} = - \frac{1}{4} \pm \frac{9}{4} = - \frac{1}{4} + \frac{9}{4}, - \frac{1}{4} - \frac{9}{4} = \frac{8}{4}, \frac{- 10}{4} = 2, \frac{- 5}{2}$

The required value of $t$ is $2, \frac{- 5}{2}$

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

Short Answer

Step by step solution

Given information

Calculation

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Solve by completing the square :4t2+2t=20

Short Answer

Step by step solution

Given information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Applied Mathematics

Statistics

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Logic and Functions

Study anywhere. Anytime. Across all devices.

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