t=-16t^2+5776

Solution for t=-16t^2+5776 equation:

Simplifying
t = -16t2 + 5776

Reorder the terms:
t = 5776 + -16t2

Solving
t = 5776 + -16t2

Solving for variable 't'.

Reorder the terms:
-5776 + t + 16t2 = 5776 + -16t2 + -5776 + 16t2

Reorder the terms:
-5776 + t + 16t2 = 5776 + -5776 + -16t2 + 16t2

Combine like terms: 5776 + -5776 = 0
-5776 + t + 16t2 = 0 + -16t2 + 16t2
-5776 + t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-5776 + t + 16t2 = 0

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

Divide each side by '16'.
-361 + 0.0625t + t2 = 0

Move the constant term to the right:

Add '361' to each side of the equation.
-361 + 0.0625t + 361 + t2 = 0 + 361

Reorder the terms:
-361 + 361 + 0.0625t + t2 = 0 + 361

Combine like terms: -361 + 361 = 0
0 + 0.0625t + t2 = 0 + 361
0.0625t + t2 = 0 + 361

Combine like terms: 0 + 361 = 361
0.0625t + t2 = 361

The t term is t.  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.
0.0625t + 0.25 + t2 = 361 + 0.25

Reorder the terms:
0.25 + 0.0625t + t2 = 361 + 0.25

Combine like terms: 361 + 0.25 = 361.25
0.25 + 0.0625t + t2 = 361.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 361.25

Calculate the square root of the right side: 19.006577809

Break this problem into two subproblems by setting 
(t + 0.5) equal to 19.006577809 and -19.006577809.

Subproblem 1
t + 0.5 = 19.006577809

Simplifying
t + 0.5 = 19.006577809

Reorder the terms:
0.5 + t = 19.006577809

Solving
0.5 + t = 19.006577809

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 = 19.006577809 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 19.006577809 + -0.5
t = 19.006577809 + -0.5

Combine like terms: 19.006577809 + -0.5 = 18.506577809
t = 18.506577809

Simplifying
t = 18.506577809

Subproblem 2
t + 0.5 = -19.006577809

Simplifying
t + 0.5 = -19.006577809

Reorder the terms:
0.5 + t = -19.006577809

Solving
0.5 + t = -19.006577809

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 = -19.006577809 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -19.006577809 + -0.5
t = -19.006577809 + -0.5

Combine like terms: -19.006577809 + -0.5 = -19.506577809
t = -19.506577809

Simplifying
t = -19.506577809

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {18.506577809, -19.506577809}