0=-16t^2-24t+130

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Solution for 0=-16t^2-24t+130 equation: 


Simplifying
0 = -16t2 + -24t + 130

Reorder the terms:
0 = 130 + -24t + -16t2

Solving
0 = 130 + -24t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -130 = -130
-130 + 24t + 16t2 = 130 + -24t + -16t2 + -130 + 24t + 16t2

Reorder the terms:
-130 + 24t + 16t2 = 130 + -130 + -24t + 24t + -16t2 + 16t2

Combine like terms: 130 + -130 = 0
-130 + 24t + 16t2 = 0 + -24t + 24t + -16t2 + 16t2
-130 + 24t + 16t2 = -24t + 24t + -16t2 + 16t2

Combine like terms: -24t + 24t = 0
-130 + 24t + 16t2 = 0 + -16t2 + 16t2
-130 + 24t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-130 + 24t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-65 + 12t + 8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-65 + 12t + 8t2)' equal to zero and attempt to solve:

Simplifying
-65 + 12t + 8t2 = 0

Solving
-65 + 12t + 8t2 = 0

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

Divide each side by '8'.
-8.125 + 1.5t + t2 = 0

Move the constant term to the right:

Add '8.125' to each side of the equation.
-8.125 + 1.5t + 8.125 + t2 = 0 + 8.125

Reorder the terms:
-8.125 + 8.125 + 1.5t + t2 = 0 + 8.125

Combine like terms: -8.125 + 8.125 = 0.000
0.000 + 1.5t + t2 = 0 + 8.125
1.5t + t2 = 0 + 8.125

Combine like terms: 0 + 8.125 = 8.125
1.5t + t2 = 8.125

The t term is 1.5t.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5t + 0.5625 + t2 = 8.125 + 0.5625

Reorder the terms:
0.5625 + 1.5t + t2 = 8.125 + 0.5625

Combine like terms: 8.125 + 0.5625 = 8.6875
0.5625 + 1.5t + t2 = 8.6875

Factor a perfect square on the left side:
(t + 0.75)(t + 0.75) = 8.6875

Calculate the square root of the right side: 2.947456531

Break this problem into two subproblems by setting 
(t + 0.75) equal to 2.947456531 and -2.947456531.


Subproblem 1
t + 0.75 = 2.947456531

Simplifying
t + 0.75 = 2.947456531

Reorder the terms:
0.75 + t = 2.947456531

Solving
0.75 + t = 2.947456531

Solving for variable 't'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + t = 2.947456531 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + t = 2.947456531 + -0.75
t = 2.947456531 + -0.75

Combine like terms: 2.947456531 + -0.75 = 2.197456531
t = 2.197456531

Simplifying
t = 2.197456531


Subproblem 2
t + 0.75 = -2.947456531

Simplifying
t + 0.75 = -2.947456531

Reorder the terms:
0.75 + t = -2.947456531

Solving
0.75 + t = -2.947456531

Solving for variable 't'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + t = -2.947456531 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + t = -2.947456531 + -0.75
t = -2.947456531 + -0.75

Combine like terms: -2.947456531 + -0.75 = -3.697456531
t = -3.697456531

Simplifying
t = -3.697456531


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.197456531, -3.697456531}
Solution
t = {2.197456531, -3.697456531}

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