-16t^2+92t+14=0

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Solution for -16t^2+92t+14=0 equation: 


Simplifying
-16t2 + 92t + 14 = 0

Reorder the terms:
14 + 92t + -16t2 = 0

Solving
14 + 92t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 46t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + 46t + -8t2)' equal to zero and attempt to solve:

Simplifying
7 + 46t + -8t2 = 0

Solving
7 + 46t + -8t2 = 0

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

Divide each side by '-8'.
-0.875 + -5.75t + t2 = 0

Move the constant term to the right:

Add '0.875' to each side of the equation.
-0.875 + -5.75t + 0.875 + t2 = 0 + 0.875

Reorder the terms:
-0.875 + 0.875 + -5.75t + t2 = 0 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + -5.75t + t2 = 0 + 0.875
-5.75t + t2 = 0 + 0.875

Combine like terms: 0 + 0.875 = 0.875
-5.75t + t2 = 0.875

The t term is -5.75t.  Take half its coefficient (-2.875).
Square it (8.265625) and add it to both sides.

Add '8.265625' to each side of the equation.
-5.75t + 8.265625 + t2 = 0.875 + 8.265625

Reorder the terms:
8.265625 + -5.75t + t2 = 0.875 + 8.265625

Combine like terms: 0.875 + 8.265625 = 9.140625
8.265625 + -5.75t + t2 = 9.140625

Factor a perfect square on the left side:
(t + -2.875)(t + -2.875) = 9.140625

Calculate the square root of the right side: 3.023346656

Break this problem into two subproblems by setting 
(t + -2.875) equal to 3.023346656 and -3.023346656.


Subproblem 1
t + -2.875 = 3.023346656

Simplifying
t + -2.875 = 3.023346656

Reorder the terms:
-2.875 + t = 3.023346656

Solving
-2.875 + t = 3.023346656

Solving for variable 't'.

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

Add '2.875' to each side of the equation.
-2.875 + 2.875 + t = 3.023346656 + 2.875

Combine like terms: -2.875 + 2.875 = 0.000
0.000 + t = 3.023346656 + 2.875
t = 3.023346656 + 2.875

Combine like terms: 3.023346656 + 2.875 = 5.898346656
t = 5.898346656

Simplifying
t = 5.898346656


Subproblem 2
t + -2.875 = -3.023346656

Simplifying
t + -2.875 = -3.023346656

Reorder the terms:
-2.875 + t = -3.023346656

Solving
-2.875 + t = -3.023346656

Solving for variable 't'.

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

Add '2.875' to each side of the equation.
-2.875 + 2.875 + t = -3.023346656 + 2.875

Combine like terms: -2.875 + 2.875 = 0.000
0.000 + t = -3.023346656 + 2.875
t = -3.023346656 + 2.875

Combine like terms: -3.023346656 + 2.875 = -0.148346656
t = -0.148346656

Simplifying
t = -0.148346656


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.898346656, -0.148346656}
Solution
t = {5.898346656, -0.148346656}

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