t^2-3t+1.25=0

Solution for t^2-3t+1.25=0 equation:

Simplifying
t2 + -3t + 1.25 = 0

Reorder the terms:
1.25 + -3t + t2 = 0

Solving
1.25 + -3t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -3t + -1.25 + t2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -3t + t2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -3t + t2 = 0 + -1.25
-3t + t2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-3t + t2 = -1.25

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = -1.25 + 2.25

Reorder the terms:
2.25 + -3t + t2 = -1.25 + 2.25

Combine like terms: -1.25 + 2.25 = 1
2.25 + -3t + t2 = 1

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(t + -1.5) equal to 1 and -1.

Subproblem 1
t + -1.5 = 1

Simplifying
t + -1.5 = 1

Reorder the terms:
-1.5 + t = 1

Solving
-1.5 + t = 1

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 1 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 1 + 1.5
t = 1 + 1.5

Combine like terms: 1 + 1.5 = 2.5
t = 2.5

Simplifying
t = 2.5

Subproblem 2
t + -1.5 = -1

Simplifying
t + -1.5 = -1

Reorder the terms:
-1.5 + t = -1

Solving
-1.5 + t = -1

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -1 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -1 + 1.5
t = -1 + 1.5

Combine like terms: -1 + 1.5 = 0.5
t = 0.5

Simplifying
t = 0.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.5, 0.5}