0=16t^2-16t-4

Solution for 0=16t^2-16t-4 equation:

Simplifying
0 = 16t2 + -16t + -4

Reorder the terms:
0 = -4 + -16t + 16t2

Solving
0 = -4 + -16t + 16t2

Solving for variable 't'.

Combine like terms: 0 + 4 = 4
4 + 16t + -16t2 = -4 + -16t + 16t2 + 4 + 16t + -16t2

Reorder the terms:
4 + 16t + -16t2 = -4 + 4 + -16t + 16t + 16t2 + -16t2

Combine like terms: -4 + 4 = 0
4 + 16t + -16t2 = 0 + -16t + 16t + 16t2 + -16t2
4 + 16t + -16t2 = -16t + 16t + 16t2 + -16t2

Combine like terms: -16t + 16t = 0
4 + 16t + -16t2 = 0 + 16t2 + -16t2
4 + 16t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
4 + 16t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 4t + -4t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + 4t + -4t2)' equal to zero and attempt to solve:

Simplifying
1 + 4t + -4t2 = 0

Solving
1 + 4t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.25 + -1t + t2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -1t + 0.25 + t2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -1t + t2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -1t + t2 = 0 + 0.25
-1t + t2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-1t + t2 = 0.25

The t term is -1t.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1t + 0.25 + t2 = 0.25 + 0.25

Reorder the terms:
0.25 + -1t + t2 = 0.25 + 0.25

Combine like terms: 0.25 + 0.25 = 0.5
0.25 + -1t + t2 = 0.5

Factor a perfect square on the left side:
(t + -0.5)(t + -0.5) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(t + -0.5) equal to 0.707106781 and -0.707106781.

Subproblem 1
t + -0.5 = 0.707106781

Simplifying
t + -0.5 = 0.707106781

Reorder the terms:
-0.5 + t = 0.707106781

Solving
-0.5 + t = 0.707106781

Solving for variable 't'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + t = 0.707106781 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t = 0.707106781 + 0.5
t = 0.707106781 + 0.5

Combine like terms: 0.707106781 + 0.5 = 1.207106781
t = 1.207106781

Simplifying
t = 1.207106781

Subproblem 2
t + -0.5 = -0.707106781

Simplifying
t + -0.5 = -0.707106781

Reorder the terms:
-0.5 + t = -0.707106781

Solving
-0.5 + t = -0.707106781

Solving for variable 't'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + t = -0.707106781 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t = -0.707106781 + 0.5
t = -0.707106781 + 0.5

Combine like terms: -0.707106781 + 0.5 = -0.207106781
t = -0.207106781

Simplifying
t = -0.207106781

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.207106781, -0.207106781}
Solution
t = {1.207106781, -0.207106781}