.0825t^2-.918t+1.866=0

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Solution for .0825t^2-.918t+1.866=0 equation: 


Simplifying
0.0825t2 + -0.918t + 1.866 = 0

Reorder the terms:
1.866 + -0.918t + 0.0825t2 = 0

Solving
1.866 + -0.918t + 0.0825t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
0.0825 the coefficient of the squared term: 

Divide each side by '0.0825'.
22.61818182 + -11.12727273t + t2 = 0

Move the constant term to the right:

Add '-22.61818182' to each side of the equation.
22.61818182 + -11.12727273t + -22.61818182 + t2 = 0 + -22.61818182

Reorder the terms:
22.61818182 + -22.61818182 + -11.12727273t + t2 = 0 + -22.61818182

Combine like terms: 22.61818182 + -22.61818182 = 0.00000000
0.00000000 + -11.12727273t + t2 = 0 + -22.61818182
-11.12727273t + t2 = 0 + -22.61818182

Combine like terms: 0 + -22.61818182 = -22.61818182
-11.12727273t + t2 = -22.61818182

The t term is -11.12727273t.  Take half its coefficient (-5.563636365).
Square it (30.95404960) and add it to both sides.

Add '30.95404960' to each side of the equation.
-11.12727273t + 30.95404960 + t2 = -22.61818182 + 30.95404960

Reorder the terms:
30.95404960 + -11.12727273t + t2 = -22.61818182 + 30.95404960

Combine like terms: -22.61818182 + 30.95404960 = 8.33586778
30.95404960 + -11.12727273t + t2 = 8.33586778

Factor a perfect square on the left side:
(t + -5.563636365)(t + -5.563636365) = 8.33586778

Calculate the square root of the right side: 2.887190292

Break this problem into two subproblems by setting 
(t + -5.563636365) equal to 2.887190292 and -2.887190292.


Subproblem 1
t + -5.563636365 = 2.887190292

Simplifying
t + -5.563636365 = 2.887190292

Reorder the terms:
-5.563636365 + t = 2.887190292

Solving
-5.563636365 + t = 2.887190292

Solving for variable 't'.

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

Add '5.563636365' to each side of the equation.
-5.563636365 + 5.563636365 + t = 2.887190292 + 5.563636365

Combine like terms: -5.563636365 + 5.563636365 = 0.000000000
0.000000000 + t = 2.887190292 + 5.563636365
t = 2.887190292 + 5.563636365

Combine like terms: 2.887190292 + 5.563636365 = 8.450826657
t = 8.450826657

Simplifying
t = 8.450826657


Subproblem 2
t + -5.563636365 = -2.887190292

Simplifying
t + -5.563636365 = -2.887190292

Reorder the terms:
-5.563636365 + t = -2.887190292

Solving
-5.563636365 + t = -2.887190292

Solving for variable 't'.

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

Add '5.563636365' to each side of the equation.
-5.563636365 + 5.563636365 + t = -2.887190292 + 5.563636365

Combine like terms: -5.563636365 + 5.563636365 = 0.000000000
0.000000000 + t = -2.887190292 + 5.563636365
t = -2.887190292 + 5.563636365

Combine like terms: -2.887190292 + 5.563636365 = 2.676446073
t = 2.676446073

Simplifying
t = 2.676446073


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.450826657, 2.676446073}

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