11x^2-22x-2=0

Solution for 11x^2-22x-2=0 equation:

Simplifying
11x2 + -22x + -2 = 0

Reorder the terms:
-2 + -22x + 11x2 = 0

Solving
-2 + -22x + 11x2 = 0

Solving for variable 'x'.

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

Divide each side by '11'.
-0.1818181818 + -2x + x2 = 0

Move the constant term to the right:

Add '0.1818181818' to each side of the equation.
-0.1818181818 + -2x + 0.1818181818 + x2 = 0 + 0.1818181818

Reorder the terms:
-0.1818181818 + 0.1818181818 + -2x + x2 = 0 + 0.1818181818

Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + 0.1818181818
-2x + x2 = 0 + 0.1818181818

Combine like terms: 0 + 0.1818181818 = 0.1818181818
-2x + x2 = 0.1818181818

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 0.1818181818 + 1

Reorder the terms:
1 + -2x + x2 = 0.1818181818 + 1

Combine like terms: 0.1818181818 + 1 = 1.1818181818
1 + -2x + x2 = 1.1818181818

Factor a perfect square on the left side:
(x + -1)(x + -1) = 1.1818181818

Calculate the square root of the right side: 1.087114613

Break this problem into two subproblems by setting 
(x + -1) equal to 1.087114613 and -1.087114613.

Subproblem 1
x + -1 = 1.087114613

Simplifying
x + -1 = 1.087114613

Reorder the terms:
-1 + x = 1.087114613

Solving
-1 + x = 1.087114613

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.087114613 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.087114613 + 1
x = 1.087114613 + 1

Combine like terms: 1.087114613 + 1 = 2.087114613
x = 2.087114613

Simplifying
x = 2.087114613

Subproblem 2
x + -1 = -1.087114613

Simplifying
x + -1 = -1.087114613

Reorder the terms:
-1 + x = -1.087114613

Solving
-1 + x = -1.087114613

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.087114613 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.087114613 + 1
x = -1.087114613 + 1

Combine like terms: -1.087114613 + 1 = -0.087114613
x = -0.087114613

Simplifying
x = -0.087114613

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.087114613, -0.087114613}