27.5=2.2(t)+0.5(1.73)t^2

Solution for 27.5=2.2(t)+0.5(1.73)t^2 equation:

Simplifying
27.5 = 2.2(t) + 0.5(1.73) * t2

Multiply 0.5 * 1.73
27.5 = 2.2t + 0.865t2

Solving
27.5 = 2.2t + 0.865t2

Solving for variable 't'.

Reorder the terms:
27.5 + -2.2t + -0.865t2 = 2.2t + -2.2t + 0.865t2 + -0.865t2

Combine like terms: 2.2t + -2.2t = 0.0
27.5 + -2.2t + -0.865t2 = 0.0 + 0.865t2 + -0.865t2
27.5 + -2.2t + -0.865t2 = 0.865t2 + -0.865t2

Combine like terms: 0.865t2 + -0.865t2 = 0.000
27.5 + -2.2t + -0.865t2 = 0.000

Begin completing the square.  Divide all terms by
-0.865 the coefficient of the squared term: 

Divide each side by '-0.865'.
-31.79190751 + 2.543352601t + t2 = 0

Move the constant term to the right:

Add '31.79190751' to each side of the equation.
-31.79190751 + 2.543352601t + 31.79190751 + t2 = 0 + 31.79190751

Reorder the terms:
-31.79190751 + 31.79190751 + 2.543352601t + t2 = 0 + 31.79190751

Combine like terms: -31.79190751 + 31.79190751 = 0.00000000
0.00000000 + 2.543352601t + t2 = 0 + 31.79190751
2.543352601t + t2 = 0 + 31.79190751

Combine like terms: 0 + 31.79190751 = 31.79190751
2.543352601t + t2 = 31.79190751

The t term is 2.543352601t.  Take half its coefficient (1.271676301).
Square it (1.617160615) and add it to both sides.

Add '1.617160615' to each side of the equation.
2.543352601t + 1.617160615 + t2 = 31.79190751 + 1.617160615

Reorder the terms:
1.617160615 + 2.543352601t + t2 = 31.79190751 + 1.617160615

Combine like terms: 31.79190751 + 1.617160615 = 33.409068125
1.617160615 + 2.543352601t + t2 = 33.409068125

Factor a perfect square on the left side:
(t + 1.271676301)(t + 1.271676301) = 33.409068125

Calculate the square root of the right side: 5.780057796

Break this problem into two subproblems by setting 
(t + 1.271676301) equal to 5.780057796 and -5.780057796.

Subproblem 1
t + 1.271676301 = 5.780057796

Simplifying
t + 1.271676301 = 5.780057796

Reorder the terms:
1.271676301 + t = 5.780057796

Solving
1.271676301 + t = 5.780057796

Solving for variable 't'.

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

Add '-1.271676301' to each side of the equation.
1.271676301 + -1.271676301 + t = 5.780057796 + -1.271676301

Combine like terms: 1.271676301 + -1.271676301 = 0.000000000
0.000000000 + t = 5.780057796 + -1.271676301
t = 5.780057796 + -1.271676301

Combine like terms: 5.780057796 + -1.271676301 = 4.508381495
t = 4.508381495

Simplifying
t = 4.508381495

Subproblem 2
t + 1.271676301 = -5.780057796

Simplifying
t + 1.271676301 = -5.780057796

Reorder the terms:
1.271676301 + t = -5.780057796

Solving
1.271676301 + t = -5.780057796

Solving for variable 't'.

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

Add '-1.271676301' to each side of the equation.
1.271676301 + -1.271676301 + t = -5.780057796 + -1.271676301

Combine like terms: 1.271676301 + -1.271676301 = 0.000000000
0.000000000 + t = -5.780057796 + -1.271676301
t = -5.780057796 + -1.271676301

Combine like terms: -5.780057796 + -1.271676301 = -7.051734097
t = -7.051734097

Simplifying
t = -7.051734097

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.508381495, -7.051734097}