0=-16t^2+104t-16

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Solution for 0=-16t^2+104t-16 equation: 


Simplifying
0 = -16t2 + 104t + -16

Reorder the terms:
0 = -16 + 104t + -16t2

Solving
0 = -16 + 104t + -16t2

Solving for variable 't'.

Combine like terms: 0 + 16 = 16
16 + -104t + 16t2 = -16 + 104t + -16t2 + 16 + -104t + 16t2

Reorder the terms:
16 + -104t + 16t2 = -16 + 16 + 104t + -104t + -16t2 + 16t2

Combine like terms: -16 + 16 = 0
16 + -104t + 16t2 = 0 + 104t + -104t + -16t2 + 16t2
16 + -104t + 16t2 = 104t + -104t + -16t2 + 16t2

Combine like terms: 104t + -104t = 0
16 + -104t + 16t2 = 0 + -16t2 + 16t2
16 + -104t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
16 + -104t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(2 + -13t + 2t2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(2 + -13t + 2t2)' equal to zero and attempt to solve:

Simplifying
2 + -13t + 2t2 = 0

Solving
2 + -13t + 2t2 = 0

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

Divide each side by '2'.
1 + -6.5t + t2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -6.5t + -1 + t2 = 0 + -1

Reorder the terms:
1 + -1 + -6.5t + t2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6.5t + t2 = 0 + -1
-6.5t + t2 = 0 + -1

Combine like terms: 0 + -1 = -1
-6.5t + t2 = -1

The t term is -6.5t.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5t + 10.5625 + t2 = -1 + 10.5625

Reorder the terms:
10.5625 + -6.5t + t2 = -1 + 10.5625

Combine like terms: -1 + 10.5625 = 9.5625
10.5625 + -6.5t + t2 = 9.5625

Factor a perfect square on the left side:
(t + -3.25)(t + -3.25) = 9.5625

Calculate the square root of the right side: 3.092329219

Break this problem into two subproblems by setting 
(t + -3.25) equal to 3.092329219 and -3.092329219.


Subproblem 1
t + -3.25 = 3.092329219

Simplifying
t + -3.25 = 3.092329219

Reorder the terms:
-3.25 + t = 3.092329219

Solving
-3.25 + t = 3.092329219

Solving for variable 't'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + t = 3.092329219 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + t = 3.092329219 + 3.25
t = 3.092329219 + 3.25

Combine like terms: 3.092329219 + 3.25 = 6.342329219
t = 6.342329219

Simplifying
t = 6.342329219


Subproblem 2
t + -3.25 = -3.092329219

Simplifying
t + -3.25 = -3.092329219

Reorder the terms:
-3.25 + t = -3.092329219

Solving
-3.25 + t = -3.092329219

Solving for variable 't'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + t = -3.092329219 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + t = -3.092329219 + 3.25
t = -3.092329219 + 3.25

Combine like terms: -3.092329219 + 3.25 = 0.157670781
t = 0.157670781

Simplifying
t = 0.157670781


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.342329219, 0.157670781}
Solution
t = {6.342329219, 0.157670781}

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