0=t^2-2t+.25

Solution for 0=t^2-2t+.25 equation:

Simplifying
0 = t2 + -2t + 0.25

Reorder the terms:
0 = 0.25 + -2t + t2

Solving
0 = 0.25 + -2t + t2

Solving for variable 't'.

Combine like terms: 0 + -0.25 = -0.25
-0.25 + 2t + -1t2 = 0.25 + -2t + t2 + -0.25 + 2t + -1t2

Reorder the terms:
-0.25 + 2t + -1t2 = 0.25 + -0.25 + -2t + 2t + t2 + -1t2

Combine like terms: 0.25 + -0.25 = 0.00
-0.25 + 2t + -1t2 = 0.00 + -2t + 2t + t2 + -1t2
-0.25 + 2t + -1t2 = -2t + 2t + t2 + -1t2

Combine like terms: -2t + 2t = 0
-0.25 + 2t + -1t2 = 0 + t2 + -1t2
-0.25 + 2t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-0.25 + 2t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
0.25 + -2t + t2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -2t + -0.25 + t2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -2t + t2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -2t + t2 = 0 + -0.25
-2t + t2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-2t + t2 = -0.25

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = -0.25 + 1

Reorder the terms:
1 + -2t + t2 = -0.25 + 1

Combine like terms: -0.25 + 1 = 0.75
1 + -2t + t2 = 0.75

Factor a perfect square on the left side:
(t + -1)(t + -1) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(t + -1) equal to 0.866025404 and -0.866025404.

Subproblem 1
t + -1 = 0.866025404

Simplifying
t + -1 = 0.866025404

Reorder the terms:
-1 + t = 0.866025404

Solving
-1 + t = 0.866025404

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = 0.866025404 + 1

Combine like terms: -1 + 1 = 0
0 + t = 0.866025404 + 1
t = 0.866025404 + 1

Combine like terms: 0.866025404 + 1 = 1.866025404
t = 1.866025404

Simplifying
t = 1.866025404

Subproblem 2
t + -1 = -0.866025404

Simplifying
t + -1 = -0.866025404

Reorder the terms:
-1 + t = -0.866025404

Solving
-1 + t = -0.866025404

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = -0.866025404 + 1

Combine like terms: -1 + 1 = 0
0 + t = -0.866025404 + 1
t = -0.866025404 + 1

Combine like terms: -0.866025404 + 1 = 0.133974596
t = 0.133974596

Simplifying
t = 0.133974596

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.866025404, 0.133974596}