6.5=t^2-5t+6.25

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Solution for 6.5=t^2-5t+6.25 equation: 


Simplifying
6.5 = t2 + -5t + 6.25

Reorder the terms:
6.5 = 6.25 + -5t + t2

Solving
6.5 = 6.25 + -5t + t2

Solving for variable 't'.

Combine like terms: 6.5 + -6.25 = 0.25
0.25 + 5t + -1t2 = 6.25 + -5t + t2 + -6.25 + 5t + -1t2

Reorder the terms:
0.25 + 5t + -1t2 = 6.25 + -6.25 + -5t + 5t + t2 + -1t2

Combine like terms: 6.25 + -6.25 = 0.00
0.25 + 5t + -1t2 = 0.00 + -5t + 5t + t2 + -1t2
0.25 + 5t + -1t2 = -5t + 5t + t2 + -1t2

Combine like terms: -5t + 5t = 0
0.25 + 5t + -1t2 = 0 + t2 + -1t2
0.25 + 5t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
0.25 + 5t + -1t2 = 0

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

Divide each side by '-1'.
-0.25 + -5t + t2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -5t + 0.25 + t2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -5t + t2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -5t + t2 = 0 + 0.25
-5t + t2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-5t + t2 = 0.25

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 = 0.25 + 6.25

Reorder the terms:
6.25 + -5t + t2 = 0.25 + 6.25

Combine like terms: 0.25 + 6.25 = 6.5
6.25 + -5t + t2 = 6.5

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 6.5

Calculate the square root of the right side: 2.549509757

Break this problem into two subproblems by setting 
(t + -2.5) equal to 2.549509757 and -2.549509757.


Subproblem 1
t + -2.5 = 2.549509757

Simplifying
t + -2.5 = 2.549509757

Reorder the terms:
-2.5 + t = 2.549509757

Solving
-2.5 + t = 2.549509757

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 = 2.549509757 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 2.549509757 + 2.5
t = 2.549509757 + 2.5

Combine like terms: 2.549509757 + 2.5 = 5.049509757
t = 5.049509757

Simplifying
t = 5.049509757


Subproblem 2
t + -2.5 = -2.549509757

Simplifying
t + -2.5 = -2.549509757

Reorder the terms:
-2.5 + t = -2.549509757

Solving
-2.5 + t = -2.549509757

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 = -2.549509757 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -2.549509757 + 2.5
t = -2.549509757 + 2.5

Combine like terms: -2.549509757 + 2.5 = -0.049509757
t = -0.049509757

Simplifying
t = -0.049509757


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.049509757, -0.049509757}

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