1.1*x^2+5.5*x+6.6=0

Solution for 1.1*x^2+5.5*x+6.6=0 equation:

Simplifying
1.1x2 + 5.5x + 6.6 = 0

Reorder the terms:
6.6 + 5.5x + 1.1x2 = 0

Solving
6.6 + 5.5x + 1.1x2 = 0

Solving for variable 'x'.

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

Divide each side by '1.1'.
6 + 5x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 5x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 5x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5x + x2 = 0 + -6
5x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
5x + x2 = -6

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -6 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -6 + 6.25

Combine like terms: -6 + 6.25 = 0.25
6.25 + 5x + x2 = 0.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 0.25

Calculate the square root of the right side: 0.5

Break this problem into two subproblems by setting 
(x + 2.5) equal to 0.5 and -0.5.

Subproblem 1
x + 2.5 = 0.5

Simplifying
x + 2.5 = 0.5

Reorder the terms:
2.5 + x = 0.5

Solving
2.5 + x = 0.5

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 0.5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 0.5 + -2.5
x = 0.5 + -2.5

Combine like terms: 0.5 + -2.5 = -2
x = -2

Simplifying
x = -2

Subproblem 2
x + 2.5 = -0.5

Simplifying
x + 2.5 = -0.5

Reorder the terms:
2.5 + x = -0.5

Solving
2.5 + x = -0.5

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -0.5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -0.5 + -2.5
x = -0.5 + -2.5

Combine like terms: -0.5 + -2.5 = -3
x = -3

Simplifying
x = -3

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2, -3}