t^2+5.5t-20=0

Solution for t^2+5.5t-20=0 equation:

Simplifying
t2 + 5.5t + -20 = 0

Reorder the terms:
-20 + 5.5t + t2 = 0

Solving
-20 + 5.5t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 5.5t + 20 + t2 = 0 + 20

Reorder the terms:
-20 + 20 + 5.5t + t2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 5.5t + t2 = 0 + 20
5.5t + t2 = 0 + 20

Combine like terms: 0 + 20 = 20
5.5t + t2 = 20

The t term is 5.5t.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5t + 7.5625 + t2 = 20 + 7.5625

Reorder the terms:
7.5625 + 5.5t + t2 = 20 + 7.5625

Combine like terms: 20 + 7.5625 = 27.5625
7.5625 + 5.5t + t2 = 27.5625

Factor a perfect square on the left side:
(t + 2.75)(t + 2.75) = 27.5625

Calculate the square root of the right side: 5.25

Break this problem into two subproblems by setting 
(t + 2.75) equal to 5.25 and -5.25.

Subproblem 1
t + 2.75 = 5.25

Simplifying
t + 2.75 = 5.25

Reorder the terms:
2.75 + t = 5.25

Solving
2.75 + t = 5.25

Solving for variable 't'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + t = 5.25 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + t = 5.25 + -2.75
t = 5.25 + -2.75

Combine like terms: 5.25 + -2.75 = 2.5
t = 2.5

Simplifying
t = 2.5

Subproblem 2
t + 2.75 = -5.25

Simplifying
t + 2.75 = -5.25

Reorder the terms:
2.75 + t = -5.25

Solving
2.75 + t = -5.25

Solving for variable 't'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + t = -5.25 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + t = -5.25 + -2.75
t = -5.25 + -2.75

Combine like terms: -5.25 + -2.75 = -8
t = -8

Simplifying
t = -8

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.5, -8}