550=-16t^2-20t+1100

Solution for 550=-16t^2-20t+1100 equation:

Simplifying
550 = -16t2 + -20t + 1100

Reorder the terms:
550 = 1100 + -20t + -16t2

Solving
550 = 1100 + -20t + -16t2

Solving for variable 't'.

Combine like terms: 550 + -1100 = -550
-550 + 20t + 16t2 = 1100 + -20t + -16t2 + -1100 + 20t + 16t2

Reorder the terms:
-550 + 20t + 16t2 = 1100 + -1100 + -20t + 20t + -16t2 + 16t2

Combine like terms: 1100 + -1100 = 0
-550 + 20t + 16t2 = 0 + -20t + 20t + -16t2 + 16t2
-550 + 20t + 16t2 = -20t + 20t + -16t2 + 16t2

Combine like terms: -20t + 20t = 0
-550 + 20t + 16t2 = 0 + -16t2 + 16t2
-550 + 20t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-550 + 20t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-275 + 10t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-275 + 10t + 8t2)' equal to zero and attempt to solve:

Simplifying
-275 + 10t + 8t2 = 0

Solving
-275 + 10t + 8t2 = 0

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

Divide each side by '8'.
-34.375 + 1.25t + t2 = 0

Move the constant term to the right:

Add '34.375' to each side of the equation.
-34.375 + 1.25t + 34.375 + t2 = 0 + 34.375

Reorder the terms:
-34.375 + 34.375 + 1.25t + t2 = 0 + 34.375

Combine like terms: -34.375 + 34.375 = 0.000
0.000 + 1.25t + t2 = 0 + 34.375
1.25t + t2 = 0 + 34.375

Combine like terms: 0 + 34.375 = 34.375
1.25t + t2 = 34.375

The t term is 1.25t.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25t + 0.390625 + t2 = 34.375 + 0.390625

Reorder the terms:
0.390625 + 1.25t + t2 = 34.375 + 0.390625

Combine like terms: 34.375 + 0.390625 = 34.765625
0.390625 + 1.25t + t2 = 34.765625

Factor a perfect square on the left side:
(t + 0.625)(t + 0.625) = 34.765625

Calculate the square root of the right side: 5.896238208

Break this problem into two subproblems by setting 
(t + 0.625) equal to 5.896238208 and -5.896238208.

Subproblem 1
t + 0.625 = 5.896238208

Simplifying
t + 0.625 = 5.896238208

Reorder the terms:
0.625 + t = 5.896238208

Solving
0.625 + t = 5.896238208

Solving for variable 't'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + t = 5.896238208 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + t = 5.896238208 + -0.625
t = 5.896238208 + -0.625

Combine like terms: 5.896238208 + -0.625 = 5.271238208
t = 5.271238208

Simplifying
t = 5.271238208

Subproblem 2
t + 0.625 = -5.896238208

Simplifying
t + 0.625 = -5.896238208

Reorder the terms:
0.625 + t = -5.896238208

Solving
0.625 + t = -5.896238208

Solving for variable 't'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + t = -5.896238208 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + t = -5.896238208 + -0.625
t = -5.896238208 + -0.625

Combine like terms: -5.896238208 + -0.625 = -6.521238208
t = -6.521238208

Simplifying
t = -6.521238208

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.271238208, -6.521238208}
Solution
t = {5.271238208, -6.521238208}