-16t^2-6t+130=0

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Solution for -16t^2-6t+130=0 equation: 


Simplifying
-16t2 + -6t + 130 = 0

Reorder the terms:
130 + -6t + -16t2 = 0

Solving
130 + -6t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(65 + -3t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(65 + -3t + -8t2)' equal to zero and attempt to solve:

Simplifying
65 + -3t + -8t2 = 0

Solving
65 + -3t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-8.125 + 0.375t + t2 = 0

Move the constant term to the right:

Add '8.125' to each side of the equation.
-8.125 + 0.375t + 8.125 + t2 = 0 + 8.125

Reorder the terms:
-8.125 + 8.125 + 0.375t + t2 = 0 + 8.125

Combine like terms: -8.125 + 8.125 = 0.000
0.000 + 0.375t + t2 = 0 + 8.125
0.375t + t2 = 0 + 8.125

Combine like terms: 0 + 8.125 = 8.125
0.375t + t2 = 8.125

The t term is 0.375t.  Take half its coefficient (0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
0.375t + 0.03515625 + t2 = 8.125 + 0.03515625

Reorder the terms:
0.03515625 + 0.375t + t2 = 8.125 + 0.03515625

Combine like terms: 8.125 + 0.03515625 = 8.16015625
0.03515625 + 0.375t + t2 = 8.16015625

Factor a perfect square on the left side:
(t + 0.1875)(t + 0.1875) = 8.16015625

Calculate the square root of the right side: 2.856598721

Break this problem into two subproblems by setting 
(t + 0.1875) equal to 2.856598721 and -2.856598721.


Subproblem 1
t + 0.1875 = 2.856598721

Simplifying
t + 0.1875 = 2.856598721

Reorder the terms:
0.1875 + t = 2.856598721

Solving
0.1875 + t = 2.856598721

Solving for variable 't'.

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

Add '-0.1875' to each side of the equation.
0.1875 + -0.1875 + t = 2.856598721 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + t = 2.856598721 + -0.1875
t = 2.856598721 + -0.1875

Combine like terms: 2.856598721 + -0.1875 = 2.669098721
t = 2.669098721

Simplifying
t = 2.669098721


Subproblem 2
t + 0.1875 = -2.856598721

Simplifying
t + 0.1875 = -2.856598721

Reorder the terms:
0.1875 + t = -2.856598721

Solving
0.1875 + t = -2.856598721

Solving for variable 't'.

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

Add '-0.1875' to each side of the equation.
0.1875 + -0.1875 + t = -2.856598721 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + t = -2.856598721 + -0.1875
t = -2.856598721 + -0.1875

Combine like terms: -2.856598721 + -0.1875 = -3.044098721
t = -3.044098721

Simplifying
t = -3.044098721


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.669098721, -3.044098721}
Solution
t = {2.669098721, -3.044098721}

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