(16t^2-12t-1538)=0

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Solution for (16t^2-12t-1538)=0 equation: 


Simplifying
(16t2 + -12t + -1538) = 0

Reorder the terms:
(-1538 + -12t + 16t2) = 0

Remove parenthesis around (-1538 + -12t + 16t2)
-1538 + -12t + 16t2 = 0

Solving
-1538 + -12t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-769 + -6t + 8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-769 + -6t + 8t2)' equal to zero and attempt to solve:

Simplifying
-769 + -6t + 8t2 = 0

Solving
-769 + -6t + 8t2 = 0

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

Divide each side by '8'.
-96.125 + -0.75t + t2 = 0

Move the constant term to the right:

Add '96.125' to each side of the equation.
-96.125 + -0.75t + 96.125 + t2 = 0 + 96.125

Reorder the terms:
-96.125 + 96.125 + -0.75t + t2 = 0 + 96.125

Combine like terms: -96.125 + 96.125 = 0.000
0.000 + -0.75t + t2 = 0 + 96.125
-0.75t + t2 = 0 + 96.125

Combine like terms: 0 + 96.125 = 96.125
-0.75t + t2 = 96.125

The t term is -0.75t.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75t + 0.140625 + t2 = 96.125 + 0.140625

Reorder the terms:
0.140625 + -0.75t + t2 = 96.125 + 0.140625

Combine like terms: 96.125 + 0.140625 = 96.265625
0.140625 + -0.75t + t2 = 96.265625

Factor a perfect square on the left side:
(t + -0.375)(t + -0.375) = 96.265625

Calculate the square root of the right side: 9.811504727

Break this problem into two subproblems by setting 
(t + -0.375) equal to 9.811504727 and -9.811504727.


Subproblem 1
t + -0.375 = 9.811504727

Simplifying
t + -0.375 = 9.811504727

Reorder the terms:
-0.375 + t = 9.811504727

Solving
-0.375 + t = 9.811504727

Solving for variable 't'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + t = 9.811504727 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + t = 9.811504727 + 0.375
t = 9.811504727 + 0.375

Combine like terms: 9.811504727 + 0.375 = 10.186504727
t = 10.186504727

Simplifying
t = 10.186504727


Subproblem 2
t + -0.375 = -9.811504727

Simplifying
t + -0.375 = -9.811504727

Reorder the terms:
-0.375 + t = -9.811504727

Solving
-0.375 + t = -9.811504727

Solving for variable 't'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + t = -9.811504727 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + t = -9.811504727 + 0.375
t = -9.811504727 + 0.375

Combine like terms: -9.811504727 + 0.375 = -9.436504727
t = -9.436504727

Simplifying
t = -9.436504727


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {10.186504727, -9.436504727}
Solution
t = {10.186504727, -9.436504727}

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