0=1+16t+4t^2

Solution for 0=1+16t+4t^2 equation:

Simplifying
0 = 1 + 16t + 4t2

Solving
0 = 1 + 16t + 4t2

Solving for variable 't'.

Combine like terms: 0 + -1 = -1
-1 + -16t + -4t2 = 1 + 16t + 4t2 + -1 + -16t + -4t2

Reorder the terms:
-1 + -16t + -4t2 = 1 + -1 + 16t + -16t + 4t2 + -4t2

Combine like terms: 1 + -1 = 0
-1 + -16t + -4t2 = 0 + 16t + -16t + 4t2 + -4t2
-1 + -16t + -4t2 = 16t + -16t + 4t2 + -4t2

Combine like terms: 16t + -16t = 0
-1 + -16t + -4t2 = 0 + 4t2 + -4t2
-1 + -16t + -4t2 = 4t2 + -4t2

Combine like terms: 4t2 + -4t2 = 0
-1 + -16t + -4t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 16t + 4t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 16t + 4t2)' equal to zero and attempt to solve:

Simplifying
1 + 16t + 4t2 = 0

Solving
1 + 16t + 4t2 = 0

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

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

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 4t + -0.25 + t2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 4t + t2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 4t + t2 = 0 + -0.25
4t + t2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
4t + t2 = -0.25

The t term is 4t.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4t + 4 + t2 = -0.25 + 4

Reorder the terms:
4 + 4t + t2 = -0.25 + 4

Combine like terms: -0.25 + 4 = 3.75
4 + 4t + t2 = 3.75

Factor a perfect square on the left side:
(t + 2)(t + 2) = 3.75

Calculate the square root of the right side: 1.936491673

Break this problem into two subproblems by setting 
(t + 2) equal to 1.936491673 and -1.936491673.

Subproblem 1
t + 2 = 1.936491673

Simplifying
t + 2 = 1.936491673

Reorder the terms:
2 + t = 1.936491673

Solving
2 + t = 1.936491673

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = 1.936491673 + -2

Combine like terms: 2 + -2 = 0
0 + t = 1.936491673 + -2
t = 1.936491673 + -2

Combine like terms: 1.936491673 + -2 = -0.063508327
t = -0.063508327

Simplifying
t = -0.063508327

Subproblem 2
t + 2 = -1.936491673

Simplifying
t + 2 = -1.936491673

Reorder the terms:
2 + t = -1.936491673

Solving
2 + t = -1.936491673

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = -1.936491673 + -2

Combine like terms: 2 + -2 = 0
0 + t = -1.936491673 + -2
t = -1.936491673 + -2

Combine like terms: -1.936491673 + -2 = -3.936491673
t = -3.936491673

Simplifying
t = -3.936491673

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.063508327, -3.936491673}
Solution
t = {-0.063508327, -3.936491673}