2=-16t^2+80t-6

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Solution for 2=-16t^2+80t-6 equation: 


Simplifying
2 = -16t2 + 80t + -6

Reorder the terms:
2 = -6 + 80t + -16t2

Solving
2 = -6 + 80t + -16t2

Solving for variable 't'.

Combine like terms: 2 + 6 = 8
8 + -80t + 16t2 = -6 + 80t + -16t2 + 6 + -80t + 16t2

Reorder the terms:
8 + -80t + 16t2 = -6 + 6 + 80t + -80t + -16t2 + 16t2

Combine like terms: -6 + 6 = 0
8 + -80t + 16t2 = 0 + 80t + -80t + -16t2 + 16t2
8 + -80t + 16t2 = 80t + -80t + -16t2 + 16t2

Combine like terms: 80t + -80t = 0
8 + -80t + 16t2 = 0 + -16t2 + 16t2
8 + -80t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
8 + -80t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(1 + -10t + 2t2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(1 + -10t + 2t2)' equal to zero and attempt to solve:

Simplifying
1 + -10t + 2t2 = 0

Solving
1 + -10t + 2t2 = 0

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

Divide each side by '2'.
0.5 + -5t + t2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -5t + -0.5 + t2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -5t + t2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -5t + t2 = 0 + -0.5
-5t + t2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-5t + t2 = -0.5

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 = -0.5 + 6.25

Reorder the terms:
6.25 + -5t + t2 = -0.5 + 6.25

Combine like terms: -0.5 + 6.25 = 5.75
6.25 + -5t + t2 = 5.75

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(t + -2.5) equal to 2.397915762 and -2.397915762.


Subproblem 1
t + -2.5 = 2.397915762

Simplifying
t + -2.5 = 2.397915762

Reorder the terms:
-2.5 + t = 2.397915762

Solving
-2.5 + t = 2.397915762

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 = 2.397915762 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 2.397915762 + 2.5
t = 2.397915762 + 2.5

Combine like terms: 2.397915762 + 2.5 = 4.897915762
t = 4.897915762

Simplifying
t = 4.897915762


Subproblem 2
t + -2.5 = -2.397915762

Simplifying
t + -2.5 = -2.397915762

Reorder the terms:
-2.5 + t = -2.397915762

Solving
-2.5 + t = -2.397915762

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 = -2.397915762 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -2.397915762 + 2.5
t = -2.397915762 + 2.5

Combine like terms: -2.397915762 + 2.5 = 0.102084238
t = 0.102084238

Simplifying
t = 0.102084238


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.897915762, 0.102084238}
Solution
t = {4.897915762, 0.102084238}

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