t=16t^2+200t+4

Solution for t=16t^2+200t+4 equation:

Simplifying
t = 16t2 + 200t + 4

Reorder the terms:
t = 4 + 200t + 16t2

Solving
t = 4 + 200t + 16t2

Solving for variable 't'.

Reorder the terms:
-4 + t + -200t + -16t2 = 4 + 200t + 16t2 + -4 + -200t + -16t2

Combine like terms: t + -200t = -199t
-4 + -199t + -16t2 = 4 + 200t + 16t2 + -4 + -200t + -16t2

Reorder the terms:
-4 + -199t + -16t2 = 4 + -4 + 200t + -200t + 16t2 + -16t2

Combine like terms: 4 + -4 = 0
-4 + -199t + -16t2 = 0 + 200t + -200t + 16t2 + -16t2
-4 + -199t + -16t2 = 200t + -200t + 16t2 + -16t2

Combine like terms: 200t + -200t = 0
-4 + -199t + -16t2 = 0 + 16t2 + -16t2
-4 + -199t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-4 + -199t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 199t + 16t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(4 + 199t + 16t2)' equal to zero and attempt to solve:

Simplifying
4 + 199t + 16t2 = 0

Solving
4 + 199t + 16t2 = 0

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

Divide each side by '16'.
0.25 + 12.4375t + t2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 12.4375t + -0.25 + t2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 12.4375t + t2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 12.4375t + t2 = 0 + -0.25
12.4375t + t2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
12.4375t + t2 = -0.25

The t term is 12.4375t.  Take half its coefficient (6.21875).
Square it (38.67285156) and add it to both sides.

Add '38.67285156' to each side of the equation.
12.4375t + 38.67285156 + t2 = -0.25 + 38.67285156

Reorder the terms:
38.67285156 + 12.4375t + t2 = -0.25 + 38.67285156

Combine like terms: -0.25 + 38.67285156 = 38.42285156
38.67285156 + 12.4375t + t2 = 38.42285156

Factor a perfect square on the left side:
(t + 6.21875)(t + 6.21875) = 38.42285156

Calculate the square root of the right side: 6.198616907

Break this problem into two subproblems by setting 
(t + 6.21875) equal to 6.198616907 and -6.198616907.

Subproblem 1
t + 6.21875 = 6.198616907

Simplifying
t + 6.21875 = 6.198616907

Reorder the terms:
6.21875 + t = 6.198616907

Solving
6.21875 + t = 6.198616907

Solving for variable 't'.

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

Add '-6.21875' to each side of the equation.
6.21875 + -6.21875 + t = 6.198616907 + -6.21875

Combine like terms: 6.21875 + -6.21875 = 0.00000
0.00000 + t = 6.198616907 + -6.21875
t = 6.198616907 + -6.21875

Combine like terms: 6.198616907 + -6.21875 = -0.020133093
t = -0.020133093

Simplifying
t = -0.020133093

Subproblem 2
t + 6.21875 = -6.198616907

Simplifying
t + 6.21875 = -6.198616907

Reorder the terms:
6.21875 + t = -6.198616907

Solving
6.21875 + t = -6.198616907

Solving for variable 't'.

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

Add '-6.21875' to each side of the equation.
6.21875 + -6.21875 + t = -6.198616907 + -6.21875

Combine like terms: 6.21875 + -6.21875 = 0.00000
0.00000 + t = -6.198616907 + -6.21875
t = -6.198616907 + -6.21875

Combine like terms: -6.198616907 + -6.21875 = -12.417366907
t = -12.417366907

Simplifying
t = -12.417366907

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.020133093, -12.417366907}
Solution
t = {-0.020133093, -12.417366907}