20.202t^2-153.54t+124.76=0

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Solution for 20.202t^2-153.54t+124.76=0 equation: 


Simplifying
20.202t2 + -153.54t + 124.76 = 0

Reorder the terms:
124.76 + -153.54t + 20.202t2 = 0

Solving
124.76 + -153.54t + 20.202t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
20.202 the coefficient of the squared term: 

Divide each side by '20.202'.
6.175626176 + -7.6002376t + t2 = 0

Move the constant term to the right:

Add '-6.175626176' to each side of the equation.
6.175626176 + -7.6002376t + -6.175626176 + t2 = 0 + -6.175626176

Reorder the terms:
6.175626176 + -6.175626176 + -7.6002376t + t2 = 0 + -6.175626176

Combine like terms: 6.175626176 + -6.175626176 = 0.000000000
0.000000000 + -7.6002376t + t2 = 0 + -6.175626176
-7.6002376t + t2 = 0 + -6.175626176

Combine like terms: 0 + -6.175626176 = -6.175626176
-7.6002376t + t2 = -6.175626176

The t term is -7.6002376t.  Take half its coefficient (-3.8001188).
Square it (14.44090289) and add it to both sides.

Add '14.44090289' to each side of the equation.
-7.6002376t + 14.44090289 + t2 = -6.175626176 + 14.44090289

Reorder the terms:
14.44090289 + -7.6002376t + t2 = -6.175626176 + 14.44090289

Combine like terms: -6.175626176 + 14.44090289 = 8.265276714
14.44090289 + -7.6002376t + t2 = 8.265276714

Factor a perfect square on the left side:
(t + -3.8001188)(t + -3.8001188) = 8.265276714

Calculate the square root of the right side: 2.874939428

Break this problem into two subproblems by setting 
(t + -3.8001188) equal to 2.874939428 and -2.874939428.


Subproblem 1
t + -3.8001188 = 2.874939428

Simplifying
t + -3.8001188 = 2.874939428

Reorder the terms:
-3.8001188 + t = 2.874939428

Solving
-3.8001188 + t = 2.874939428

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '3.8001188' to each side of the equation.
-3.8001188 + 3.8001188 + t = 2.874939428 + 3.8001188

Combine like terms: -3.8001188 + 3.8001188 = 0.0000000
0.0000000 + t = 2.874939428 + 3.8001188
t = 2.874939428 + 3.8001188

Combine like terms: 2.874939428 + 3.8001188 = 6.675058228
t = 6.675058228

Simplifying
t = 6.675058228


Subproblem 2
t + -3.8001188 = -2.874939428

Simplifying
t + -3.8001188 = -2.874939428

Reorder the terms:
-3.8001188 + t = -2.874939428

Solving
-3.8001188 + t = -2.874939428

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '3.8001188' to each side of the equation.
-3.8001188 + 3.8001188 + t = -2.874939428 + 3.8001188

Combine like terms: -3.8001188 + 3.8001188 = 0.0000000
0.0000000 + t = -2.874939428 + 3.8001188
t = -2.874939428 + 3.8001188

Combine like terms: -2.874939428 + 3.8001188 = 0.925179372
t = 0.925179372

Simplifying
t = 0.925179372


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.675058228, 0.925179372}

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