-0.8t^2+4t-2.5=0

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Solution for -0.8t^2+4t-2.5=0 equation: 


Simplifying
-0.8t2 + 4t + -2.5 = 0

Reorder the terms:
-2.5 + 4t + -0.8t2 = 0

Solving
-2.5 + 4t + -0.8t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-0.8 the coefficient of the squared term: 

Divide each side by '-0.8'.
3.125 + -5t + t2 = 0

Move the constant term to the right:

Add '-3.125' to each side of the equation.
3.125 + -5t + -3.125 + t2 = 0 + -3.125

Reorder the terms:
3.125 + -3.125 + -5t + t2 = 0 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + -5t + t2 = 0 + -3.125
-5t + t2 = 0 + -3.125

Combine like terms: 0 + -3.125 = -3.125
-5t + t2 = -3.125

The t term is -5t.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5t + 6.25 + t2 = -3.125 + 6.25

Reorder the terms:
6.25 + -5t + t2 = -3.125 + 6.25

Combine like terms: -3.125 + 6.25 = 3.125
6.25 + -5t + t2 = 3.125

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 3.125

Calculate the square root of the right side: 1.767766953

Break this problem into two subproblems by setting 
(t + -2.5) equal to 1.767766953 and -1.767766953.


Subproblem 1
t + -2.5 = 1.767766953

Simplifying
t + -2.5 = 1.767766953

Reorder the terms:
-2.5 + t = 1.767766953

Solving
-2.5 + t = 1.767766953

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = 1.767766953 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 1.767766953 + 2.5
t = 1.767766953 + 2.5

Combine like terms: 1.767766953 + 2.5 = 4.267766953
t = 4.267766953

Simplifying
t = 4.267766953


Subproblem 2
t + -2.5 = -1.767766953

Simplifying
t + -2.5 = -1.767766953

Reorder the terms:
-2.5 + t = -1.767766953

Solving
-2.5 + t = -1.767766953

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = -1.767766953 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -1.767766953 + 2.5
t = -1.767766953 + 2.5

Combine like terms: -1.767766953 + 2.5 = 0.732233047
t = 0.732233047

Simplifying
t = 0.732233047


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.267766953, 0.732233047}

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