2.2t^2-19t+9.5=0

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Solution for 2.2t^2-19t+9.5=0 equation: 


Simplifying
2.2t2 + -19t + 9.5 = 0

Reorder the terms:
9.5 + -19t + 2.2t2 = 0

Solving
9.5 + -19t + 2.2t2 = 0

Solving for variable 't'.

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

Divide each side by '2.2'.
4.318181818 + -8.636363636t + t2 = 0

Move the constant term to the right:

Add '-4.318181818' to each side of the equation.
4.318181818 + -8.636363636t + -4.318181818 + t2 = 0 + -4.318181818

Reorder the terms:
4.318181818 + -4.318181818 + -8.636363636t + t2 = 0 + -4.318181818

Combine like terms: 4.318181818 + -4.318181818 = 0.000000000
0.000000000 + -8.636363636t + t2 = 0 + -4.318181818
-8.636363636t + t2 = 0 + -4.318181818

Combine like terms: 0 + -4.318181818 = -4.318181818
-8.636363636t + t2 = -4.318181818

The t term is -8.636363636t.  Take half its coefficient (-4.318181818).
Square it (18.64669421) and add it to both sides.

Add '18.64669421' to each side of the equation.
-8.636363636t + 18.64669421 + t2 = -4.318181818 + 18.64669421

Reorder the terms:
18.64669421 + -8.636363636t + t2 = -4.318181818 + 18.64669421

Combine like terms: -4.318181818 + 18.64669421 = 14.328512392
18.64669421 + -8.636363636t + t2 = 14.328512392

Factor a perfect square on the left side:
(t + -4.318181818)(t + -4.318181818) = 14.328512392

Calculate the square root of the right side: 3.785302153

Break this problem into two subproblems by setting 
(t + -4.318181818) equal to 3.785302153 and -3.785302153.


Subproblem 1
t + -4.318181818 = 3.785302153

Simplifying
t + -4.318181818 = 3.785302153

Reorder the terms:
-4.318181818 + t = 3.785302153

Solving
-4.318181818 + t = 3.785302153

Solving for variable 't'.

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

Add '4.318181818' to each side of the equation.
-4.318181818 + 4.318181818 + t = 3.785302153 + 4.318181818

Combine like terms: -4.318181818 + 4.318181818 = 0.000000000
0.000000000 + t = 3.785302153 + 4.318181818
t = 3.785302153 + 4.318181818

Combine like terms: 3.785302153 + 4.318181818 = 8.103483971
t = 8.103483971

Simplifying
t = 8.103483971


Subproblem 2
t + -4.318181818 = -3.785302153

Simplifying
t + -4.318181818 = -3.785302153

Reorder the terms:
-4.318181818 + t = -3.785302153

Solving
-4.318181818 + t = -3.785302153

Solving for variable 't'.

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

Add '4.318181818' to each side of the equation.
-4.318181818 + 4.318181818 + t = -3.785302153 + 4.318181818

Combine like terms: -4.318181818 + 4.318181818 = 0.000000000
0.000000000 + t = -3.785302153 + 4.318181818
t = -3.785302153 + 4.318181818

Combine like terms: -3.785302153 + 4.318181818 = 0.532879665
t = 0.532879665

Simplifying
t = 0.532879665


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.103483971, 0.532879665}

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