t^2-5t-6.4=0

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Solution for t^2-5t-6.4=0 equation: 


Simplifying
t2 + -5t + -6.4 = 0

Reorder the terms:
-6.4 + -5t + t2 = 0

Solving
-6.4 + -5t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '6.4' to each side of the equation.
-6.4 + -5t + 6.4 + t2 = 0 + 6.4

Reorder the terms:
-6.4 + 6.4 + -5t + t2 = 0 + 6.4

Combine like terms: -6.4 + 6.4 = 0.0
0.0 + -5t + t2 = 0 + 6.4
-5t + t2 = 0 + 6.4

Combine like terms: 0 + 6.4 = 6.4
-5t + t2 = 6.4

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 = 6.4 + 6.25

Reorder the terms:
6.25 + -5t + t2 = 6.4 + 6.25

Combine like terms: 6.4 + 6.25 = 12.65
6.25 + -5t + t2 = 12.65

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 12.65

Calculate the square root of the right side: 3.556683849

Break this problem into two subproblems by setting 
(t + -2.5) equal to 3.556683849 and -3.556683849.


Subproblem 1
t + -2.5 = 3.556683849

Simplifying
t + -2.5 = 3.556683849

Reorder the terms:
-2.5 + t = 3.556683849

Solving
-2.5 + t = 3.556683849

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 = 3.556683849 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 3.556683849 + 2.5
t = 3.556683849 + 2.5

Combine like terms: 3.556683849 + 2.5 = 6.056683849
t = 6.056683849

Simplifying
t = 6.056683849


Subproblem 2
t + -2.5 = -3.556683849

Simplifying
t + -2.5 = -3.556683849

Reorder the terms:
-2.5 + t = -3.556683849

Solving
-2.5 + t = -3.556683849

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 = -3.556683849 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -3.556683849 + 2.5
t = -3.556683849 + 2.5

Combine like terms: -3.556683849 + 2.5 = -1.056683849
t = -1.056683849

Simplifying
t = -1.056683849


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.056683849, -1.056683849}

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