-16t^2-4t+80=0

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Solution for -16t^2-4t+80=0 equation: 


Simplifying
-16t2 + -4t + 80 = 0

Reorder the terms:
80 + -4t + -16t2 = 0

Solving
80 + -4t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(20 + -1t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(20 + -1t + -4t2)' equal to zero and attempt to solve:

Simplifying
20 + -1t + -4t2 = 0

Solving
20 + -1t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-5 + 0.25t + t2 = 0

Move the constant term to the right:

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

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

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

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

The t term is 0.25t.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25t + 0.015625 + t2 = 5 + 0.015625

Reorder the terms:
0.015625 + 0.25t + t2 = 5 + 0.015625

Combine like terms: 5 + 0.015625 = 5.015625
0.015625 + 0.25t + t2 = 5.015625

Factor a perfect square on the left side:
(t + 0.125)(t + 0.125) = 5.015625

Calculate the square root of the right side: 2.239559108

Break this problem into two subproblems by setting 
(t + 0.125) equal to 2.239559108 and -2.239559108.


Subproblem 1
t + 0.125 = 2.239559108

Simplifying
t + 0.125 = 2.239559108

Reorder the terms:
0.125 + t = 2.239559108

Solving
0.125 + t = 2.239559108

Solving for variable 't'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + t = 2.239559108 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + t = 2.239559108 + -0.125
t = 2.239559108 + -0.125

Combine like terms: 2.239559108 + -0.125 = 2.114559108
t = 2.114559108

Simplifying
t = 2.114559108


Subproblem 2
t + 0.125 = -2.239559108

Simplifying
t + 0.125 = -2.239559108

Reorder the terms:
0.125 + t = -2.239559108

Solving
0.125 + t = -2.239559108

Solving for variable 't'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + t = -2.239559108 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + t = -2.239559108 + -0.125
t = -2.239559108 + -0.125

Combine like terms: -2.239559108 + -0.125 = -2.364559108
t = -2.364559108

Simplifying
t = -2.364559108


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.114559108, -2.364559108}
Solution
t = {2.114559108, -2.364559108}

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