-16t^2+45t+2.5=5.5

Solution for -16t^2+45t+2.5=5.5 equation:

Simplifying
-16t2 + 45t + 2.5 = 5.5

Reorder the terms:
2.5 + 45t + -16t2 = 5.5

Solving
2.5 + 45t + -16t2 = 5.5

Solving for variable 't'.

Reorder the terms:
2.5 + -5.5 + 45t + -16t2 = 5.5 + -5.5

Combine like terms: 2.5 + -5.5 = -3
-3 + 45t + -16t2 = 5.5 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
-3 + 45t + -16t2 = 0.0

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

Divide each side by '-16'.
0.1875 + -2.8125t + t2 = 0.0

Move the constant term to the right:

Add '-0.1875' to each side of the equation.
0.1875 + -2.8125t + -0.1875 + t2 = 0.0 + -0.1875

Reorder the terms:
0.1875 + -0.1875 + -2.8125t + t2 = 0.0 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + -2.8125t + t2 = 0.0 + -0.1875
-2.8125t + t2 = 0.0 + -0.1875

Combine like terms: 0.0 + -0.1875 = -0.1875
-2.8125t + t2 = -0.1875

The t term is -2.8125t.  Take half its coefficient (-1.40625).
Square it (1.977539063) and add it to both sides.

Add '1.977539063' to each side of the equation.
-2.8125t + 1.977539063 + t2 = -0.1875 + 1.977539063

Reorder the terms:
1.977539063 + -2.8125t + t2 = -0.1875 + 1.977539063

Combine like terms: -0.1875 + 1.977539063 = 1.790039063
1.977539063 + -2.8125t + t2 = 1.790039063

Factor a perfect square on the left side:
(t + -1.40625)(t + -1.40625) = 1.790039063

Calculate the square root of the right side: 1.337923414

Break this problem into two subproblems by setting 
(t + -1.40625) equal to 1.337923414 and -1.337923414.

Subproblem 1
t + -1.40625 = 1.337923414

Simplifying
t + -1.40625 = 1.337923414

Reorder the terms:
-1.40625 + t = 1.337923414

Solving
-1.40625 + t = 1.337923414

Solving for variable 't'.

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

Add '1.40625' to each side of the equation.
-1.40625 + 1.40625 + t = 1.337923414 + 1.40625

Combine like terms: -1.40625 + 1.40625 = 0.00000
0.00000 + t = 1.337923414 + 1.40625
t = 1.337923414 + 1.40625

Combine like terms: 1.337923414 + 1.40625 = 2.744173414
t = 2.744173414

Simplifying
t = 2.744173414

Subproblem 2
t + -1.40625 = -1.337923414

Simplifying
t + -1.40625 = -1.337923414

Reorder the terms:
-1.40625 + t = -1.337923414

Solving
-1.40625 + t = -1.337923414

Solving for variable 't'.

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

Add '1.40625' to each side of the equation.
-1.40625 + 1.40625 + t = -1.337923414 + 1.40625

Combine like terms: -1.40625 + 1.40625 = 0.00000
0.00000 + t = -1.337923414 + 1.40625
t = -1.337923414 + 1.40625

Combine like terms: -1.337923414 + 1.40625 = 0.068326586
t = 0.068326586

Simplifying
t = 0.068326586

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.744173414, 0.068326586}