5t^2-11t+2.5=0

Solution for 5t^2-11t+2.5=0 equation:

Simplifying
5t2 + -11t + 2.5 = 0

Reorder the terms:
2.5 + -11t + 5t2 = 0

Solving
2.5 + -11t + 5t2 = 0

Solving for variable 't'.

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

Divide each side by '5'.
0.5 + -2.2t + t2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -2.2t + -0.5 + t2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -2.2t + t2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -2.2t + t2 = 0 + -0.5
-2.2t + t2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-2.2t + t2 = -0.5

The t term is -2.2t.  Take half its coefficient (-1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
-2.2t + 1.21 + t2 = -0.5 + 1.21

Reorder the terms:
1.21 + -2.2t + t2 = -0.5 + 1.21

Combine like terms: -0.5 + 1.21 = 0.71
1.21 + -2.2t + t2 = 0.71

Factor a perfect square on the left side:
(t + -1.1)(t + -1.1) = 0.71

Calculate the square root of the right side: 0.842614977

Break this problem into two subproblems by setting 
(t + -1.1) equal to 0.842614977 and -0.842614977.

Subproblem 1
t + -1.1 = 0.842614977

Simplifying
t + -1.1 = 0.842614977

Reorder the terms:
-1.1 + t = 0.842614977

Solving
-1.1 + t = 0.842614977

Solving for variable 't'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + t = 0.842614977 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + t = 0.842614977 + 1.1
t = 0.842614977 + 1.1

Combine like terms: 0.842614977 + 1.1 = 1.942614977
t = 1.942614977

Simplifying
t = 1.942614977

Subproblem 2
t + -1.1 = -0.842614977

Simplifying
t + -1.1 = -0.842614977

Reorder the terms:
-1.1 + t = -0.842614977

Solving
-1.1 + t = -0.842614977

Solving for variable 't'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + t = -0.842614977 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + t = -0.842614977 + 1.1
t = -0.842614977 + 1.1

Combine like terms: -0.842614977 + 1.1 = 0.257385023
t = 0.257385023

Simplifying
t = 0.257385023

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.942614977, 0.257385023}