16t^2-196t-14=0

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Solution for 16t^2-196t-14=0 equation: 


Simplifying
16t2 + -196t + -14 = 0

Reorder the terms:
-14 + -196t + 16t2 = 0

Solving
-14 + -196t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -98t + 8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -98t + 8t2)' equal to zero and attempt to solve:

Simplifying
-7 + -98t + 8t2 = 0

Solving
-7 + -98t + 8t2 = 0

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

Divide each side by '8'.
-0.875 + -12.25t + t2 = 0

Move the constant term to the right:

Add '0.875' to each side of the equation.
-0.875 + -12.25t + 0.875 + t2 = 0 + 0.875

Reorder the terms:
-0.875 + 0.875 + -12.25t + t2 = 0 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + -12.25t + t2 = 0 + 0.875
-12.25t + t2 = 0 + 0.875

Combine like terms: 0 + 0.875 = 0.875
-12.25t + t2 = 0.875

The t term is -12.25t.  Take half its coefficient (-6.125).
Square it (37.515625) and add it to both sides.

Add '37.515625' to each side of the equation.
-12.25t + 37.515625 + t2 = 0.875 + 37.515625

Reorder the terms:
37.515625 + -12.25t + t2 = 0.875 + 37.515625

Combine like terms: 0.875 + 37.515625 = 38.390625
37.515625 + -12.25t + t2 = 38.390625

Factor a perfect square on the left side:
(t + -6.125)(t + -6.125) = 38.390625

Calculate the square root of the right side: 6.196016866

Break this problem into two subproblems by setting 
(t + -6.125) equal to 6.196016866 and -6.196016866.


Subproblem 1
t + -6.125 = 6.196016866

Simplifying
t + -6.125 = 6.196016866

Reorder the terms:
-6.125 + t = 6.196016866

Solving
-6.125 + t = 6.196016866

Solving for variable 't'.

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

Add '6.125' to each side of the equation.
-6.125 + 6.125 + t = 6.196016866 + 6.125

Combine like terms: -6.125 + 6.125 = 0.000
0.000 + t = 6.196016866 + 6.125
t = 6.196016866 + 6.125

Combine like terms: 6.196016866 + 6.125 = 12.321016866
t = 12.321016866

Simplifying
t = 12.321016866


Subproblem 2
t + -6.125 = -6.196016866

Simplifying
t + -6.125 = -6.196016866

Reorder the terms:
-6.125 + t = -6.196016866

Solving
-6.125 + t = -6.196016866

Solving for variable 't'.

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

Add '6.125' to each side of the equation.
-6.125 + 6.125 + t = -6.196016866 + 6.125

Combine like terms: -6.125 + 6.125 = 0.000
0.000 + t = -6.196016866 + 6.125
t = -6.196016866 + 6.125

Combine like terms: -6.196016866 + 6.125 = -0.071016866
t = -0.071016866

Simplifying
t = -0.071016866


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {12.321016866, -0.071016866}
Solution
t = {12.321016866, -0.071016866}

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