0.8t^2-10t-2=0

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Solution for 0.8t^2-10t-2=0 equation: 


Simplifying
0.8t2 + -10t + -2 = 0

Reorder the terms:
-2 + -10t + 0.8t2 = 0

Solving
-2 + -10t + 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'.
-2.5 + -12.5t + t2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -12.5t + 2.5 + t2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -12.5t + t2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -12.5t + t2 = 0 + 2.5
-12.5t + t2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-12.5t + t2 = 2.5

The t term is -12.5t.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5t + 39.0625 + t2 = 2.5 + 39.0625

Reorder the terms:
39.0625 + -12.5t + t2 = 2.5 + 39.0625

Combine like terms: 2.5 + 39.0625 = 41.5625
39.0625 + -12.5t + t2 = 41.5625

Factor a perfect square on the left side:
(t + -6.25)(t + -6.25) = 41.5625

Calculate the square root of the right side: 6.446898479

Break this problem into two subproblems by setting 
(t + -6.25) equal to 6.446898479 and -6.446898479.


Subproblem 1
t + -6.25 = 6.446898479

Simplifying
t + -6.25 = 6.446898479

Reorder the terms:
-6.25 + t = 6.446898479

Solving
-6.25 + t = 6.446898479

Solving for variable 't'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + t = 6.446898479 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + t = 6.446898479 + 6.25
t = 6.446898479 + 6.25

Combine like terms: 6.446898479 + 6.25 = 12.696898479
t = 12.696898479

Simplifying
t = 12.696898479


Subproblem 2
t + -6.25 = -6.446898479

Simplifying
t + -6.25 = -6.446898479

Reorder the terms:
-6.25 + t = -6.446898479

Solving
-6.25 + t = -6.446898479

Solving for variable 't'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + t = -6.446898479 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + t = -6.446898479 + 6.25
t = -6.446898479 + 6.25

Combine like terms: -6.446898479 + 6.25 = -0.196898479
t = -0.196898479

Simplifying
t = -0.196898479


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {12.696898479, -0.196898479}

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