t^2-5.102t+2.245=0

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Solution for t^2-5.102t+2.245=0 equation: 


Simplifying
t2 + -5.102t + 2.245 = 0

Reorder the terms:
2.245 + -5.102t + t2 = 0

Solving
2.245 + -5.102t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-2.245' to each side of the equation.
2.245 + -5.102t + -2.245 + t2 = 0 + -2.245

Reorder the terms:
2.245 + -2.245 + -5.102t + t2 = 0 + -2.245

Combine like terms: 2.245 + -2.245 = 0.000
0.000 + -5.102t + t2 = 0 + -2.245
-5.102t + t2 = 0 + -2.245

Combine like terms: 0 + -2.245 = -2.245
-5.102t + t2 = -2.245

The t term is -5.102t.  Take half its coefficient (-2.551).
Square it (6.507601) and add it to both sides.

Add '6.507601' to each side of the equation.
-5.102t + 6.507601 + t2 = -2.245 + 6.507601

Reorder the terms:
6.507601 + -5.102t + t2 = -2.245 + 6.507601

Combine like terms: -2.245 + 6.507601 = 4.262601
6.507601 + -5.102t + t2 = 4.262601

Factor a perfect square on the left side:
(t + -2.551)(t + -2.551) = 4.262601

Calculate the square root of the right side: 2.064606742

Break this problem into two subproblems by setting 
(t + -2.551) equal to 2.064606742 and -2.064606742.


Subproblem 1
t + -2.551 = 2.064606742

Simplifying
t + -2.551 = 2.064606742

Reorder the terms:
-2.551 + t = 2.064606742

Solving
-2.551 + t = 2.064606742

Solving for variable 't'.

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

Add '2.551' to each side of the equation.
-2.551 + 2.551 + t = 2.064606742 + 2.551

Combine like terms: -2.551 + 2.551 = 0.000
0.000 + t = 2.064606742 + 2.551
t = 2.064606742 + 2.551

Combine like terms: 2.064606742 + 2.551 = 4.615606742
t = 4.615606742

Simplifying
t = 4.615606742


Subproblem 2
t + -2.551 = -2.064606742

Simplifying
t + -2.551 = -2.064606742

Reorder the terms:
-2.551 + t = -2.064606742

Solving
-2.551 + t = -2.064606742

Solving for variable 't'.

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

Add '2.551' to each side of the equation.
-2.551 + 2.551 + t = -2.064606742 + 2.551

Combine like terms: -2.551 + 2.551 = 0.000
0.000 + t = -2.064606742 + 2.551
t = -2.064606742 + 2.551

Combine like terms: -2.064606742 + 2.551 = 0.486393258
t = 0.486393258

Simplifying
t = 0.486393258


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.615606742, 0.486393258}

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