9x^2-2x+x=6-2x

Solution for 9x^2-2x+x=6-2x equation:

Simplifying
9x2 + -2x + x = 6 + -2x

Reorder the terms:
-2x + x + 9x2 = 6 + -2x

Combine like terms: -2x + x = -1x
-1x + 9x2 = 6 + -2x

Solving
-1x + 9x2 = 6 + -2x

Solving for variable 'x'.

Reorder the terms:
-6 + -1x + 2x + 9x2 = 6 + -2x + -6 + 2x

Combine like terms: -1x + 2x = 1x
-6 + 1x + 9x2 = 6 + -2x + -6 + 2x

Reorder the terms:
-6 + 1x + 9x2 = 6 + -6 + -2x + 2x

Combine like terms: 6 + -6 = 0
-6 + 1x + 9x2 = 0 + -2x + 2x
-6 + 1x + 9x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-6 + 1x + 9x2 = 0

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

Divide each side by '9'.
-0.6666666667 + 0.1111111111x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 0.1111111111x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 0.1111111111x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 0.1111111111x + x2 = 0 + 0.6666666667
0.1111111111x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
0.1111111111x + x2 = 0.6666666667

The x term is 0.1111111111x.  Take half its coefficient (0.05555555555).
Square it (0.003086419752) and add it to both sides.

Add '0.003086419752' to each side of the equation.
0.1111111111x + 0.003086419752 + x2 = 0.6666666667 + 0.003086419752

Reorder the terms:
0.003086419752 + 0.1111111111x + x2 = 0.6666666667 + 0.003086419752

Combine like terms: 0.6666666667 + 0.003086419752 = 0.669753086452
0.003086419752 + 0.1111111111x + x2 = 0.669753086452

Factor a perfect square on the left side:
(x + 0.05555555555)(x + 0.05555555555) = 0.669753086452

Calculate the square root of the right side: 0.818384437

Break this problem into two subproblems by setting 
(x + 0.05555555555) equal to 0.818384437 and -0.818384437.

Subproblem 1
x + 0.05555555555 = 0.818384437

Simplifying
x + 0.05555555555 = 0.818384437

Reorder the terms:
0.05555555555 + x = 0.818384437

Solving
0.05555555555 + x = 0.818384437

Solving for variable 'x'.

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

Add '-0.05555555555' to each side of the equation.
0.05555555555 + -0.05555555555 + x = 0.818384437 + -0.05555555555

Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000
0.00000000000 + x = 0.818384437 + -0.05555555555
x = 0.818384437 + -0.05555555555

Combine like terms: 0.818384437 + -0.05555555555 = 0.76282888145
x = 0.76282888145

Simplifying
x = 0.76282888145

Subproblem 2
x + 0.05555555555 = -0.818384437

Simplifying
x + 0.05555555555 = -0.818384437

Reorder the terms:
0.05555555555 + x = -0.818384437

Solving
0.05555555555 + x = -0.818384437

Solving for variable 'x'.

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

Add '-0.05555555555' to each side of the equation.
0.05555555555 + -0.05555555555 + x = -0.818384437 + -0.05555555555

Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000
0.00000000000 + x = -0.818384437 + -0.05555555555
x = -0.818384437 + -0.05555555555

Combine like terms: -0.818384437 + -0.05555555555 = -0.87393999255
x = -0.87393999255

Simplifying
x = -0.87393999255

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.76282888145, -0.87393999255}