2200=(360-2t)*(5.5+0.2t)+5.5+0.1(t^2)

Solution for 2200=(360-2t)*(5.5+0.2t)+5.5+0.1(t^2) equation:

Simplifying
2200 = (360 + -2t)(5.5 + 0.2t) + 5.5 + 0.1(t2)

Multiply (360 + -2t) * (5.5 + 0.2t)
2200 = (360(5.5 + 0.2t) + -2t * (5.5 + 0.2t)) + 5.5 + 0.1(t2)
2200 = ((5.5 * 360 + 0.2t * 360) + -2t * (5.5 + 0.2t)) + 5.5 + 0.1(t2)
2200 = ((1980 + 72t) + -2t * (5.5 + 0.2t)) + 5.5 + 0.1(t2)
2200 = (1980 + 72t + (5.5 * -2t + 0.2t * -2t)) + 5.5 + 0.1(t2)
2200 = (1980 + 72t + (-11t + -0.4t2)) + 5.5 + 0.1(t2)

Combine like terms: 72t + -11t = 61t
2200 = (1980 + 61t + -0.4t2) + 5.5 + 0.1(t2)

Reorder the terms:
2200 = 1980 + 5.5 + 61t + -0.4t2 + 0.1t2

Combine like terms: 1980 + 5.5 = 1985.5
2200 = 1985.5 + 61t + -0.4t2 + 0.1t2

Combine like terms: -0.4t2 + 0.1t2 = -0.3t2
2200 = 1985.5 + 61t + -0.3t2

Solving
2200 = 1985.5 + 61t + -0.3t2

Solving for variable 't'.

Combine like terms: 2200 + -1985.5 = 214.5
214.5 + -61t + 0.3t2 = 1985.5 + 61t + -0.3t2 + -1985.5 + -61t + 0.3t2

Reorder the terms:
214.5 + -61t + 0.3t2 = 1985.5 + -1985.5 + 61t + -61t + -0.3t2 + 0.3t2

Combine like terms: 1985.5 + -1985.5 = 0.0
214.5 + -61t + 0.3t2 = 0.0 + 61t + -61t + -0.3t2 + 0.3t2
214.5 + -61t + 0.3t2 = 61t + -61t + -0.3t2 + 0.3t2

Combine like terms: 61t + -61t = 0
214.5 + -61t + 0.3t2 = 0 + -0.3t2 + 0.3t2
214.5 + -61t + 0.3t2 = -0.3t2 + 0.3t2

Combine like terms: -0.3t2 + 0.3t2 = 0.0
214.5 + -61t + 0.3t2 = 0.0

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

Divide each side by '0.3'.
715 + -203.3333333t + t2 = 0

Move the constant term to the right:

Add '-715' to each side of the equation.
715 + -203.3333333t + -715 + t2 = 0 + -715

Reorder the terms:
715 + -715 + -203.3333333t + t2 = 0 + -715

Combine like terms: 715 + -715 = 0
0 + -203.3333333t + t2 = 0 + -715
-203.3333333t + t2 = 0 + -715

Combine like terms: 0 + -715 = -715
-203.3333333t + t2 = -715

The t term is -203.3333333t.  Take half its coefficient (-101.6666667).
Square it (10336.11112) and add it to both sides.

Add '10336.11112' to each side of the equation.
-203.3333333t + 10336.11112 + t2 = -715 + 10336.11112

Reorder the terms:
10336.11112 + -203.3333333t + t2 = -715 + 10336.11112

Combine like terms: -715 + 10336.11112 = 9621.11112
10336.11112 + -203.3333333t + t2 = 9621.11112

Factor a perfect square on the left side:
(t + -101.6666667)(t + -101.6666667) = 9621.11112

Calculate the square root of the right side: 98.087262782

Break this problem into two subproblems by setting 
(t + -101.6666667) equal to 98.087262782 and -98.087262782.

Subproblem 1
t + -101.6666667 = 98.087262782

Simplifying
t + -101.6666667 = 98.087262782

Reorder the terms:
-101.6666667 + t = 98.087262782

Solving
-101.6666667 + t = 98.087262782

Solving for variable 't'.

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

Add '101.6666667' to each side of the equation.
-101.6666667 + 101.6666667 + t = 98.087262782 + 101.6666667

Combine like terms: -101.6666667 + 101.6666667 = 0.0000000
0.0000000 + t = 98.087262782 + 101.6666667
t = 98.087262782 + 101.6666667

Combine like terms: 98.087262782 + 101.6666667 = 199.753929482
t = 199.753929482

Simplifying
t = 199.753929482

Subproblem 2
t + -101.6666667 = -98.087262782

Simplifying
t + -101.6666667 = -98.087262782

Reorder the terms:
-101.6666667 + t = -98.087262782

Solving
-101.6666667 + t = -98.087262782

Solving for variable 't'.

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

Add '101.6666667' to each side of the equation.
-101.6666667 + 101.6666667 + t = -98.087262782 + 101.6666667

Combine like terms: -101.6666667 + 101.6666667 = 0.0000000
0.0000000 + t = -98.087262782 + 101.6666667
t = -98.087262782 + 101.6666667

Combine like terms: -98.087262782 + 101.6666667 = 3.579403918
t = 3.579403918

Simplifying
t = 3.579403918

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {199.753929482, 3.579403918}