11x^2-19x+6=0

Solution for 11x^2-19x+6=0 equation:

Simplifying
11x2 + -19x + 6 = 0

Reorder the terms:
6 + -19x + 11x2 = 0

Solving
6 + -19x + 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'.
0.5454545455 + -1.727272727x + x2 = 0

Move the constant term to the right:

Add '-0.5454545455' to each side of the equation.
0.5454545455 + -1.727272727x + -0.5454545455 + x2 = 0 + -0.5454545455

Reorder the terms:
0.5454545455 + -0.5454545455 + -1.727272727x + x2 = 0 + -0.5454545455

Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000
0.0000000000 + -1.727272727x + x2 = 0 + -0.5454545455
-1.727272727x + x2 = 0 + -0.5454545455

Combine like terms: 0 + -0.5454545455 = -0.5454545455
-1.727272727x + x2 = -0.5454545455

The x term is -1.727272727x.  Take half its coefficient (-0.8636363635).
Square it (0.7458677684) and add it to both sides.

Add '0.7458677684' to each side of the equation.
-1.727272727x + 0.7458677684 + x2 = -0.5454545455 + 0.7458677684

Reorder the terms:
0.7458677684 + -1.727272727x + x2 = -0.5454545455 + 0.7458677684

Combine like terms: -0.5454545455 + 0.7458677684 = 0.2004132229
0.7458677684 + -1.727272727x + x2 = 0.2004132229

Factor a perfect square on the left side:
(x + -0.8636363635)(x + -0.8636363635) = 0.2004132229

Calculate the square root of the right side: 0.447675354

Break this problem into two subproblems by setting 
(x + -0.8636363635) equal to 0.447675354 and -0.447675354.

Subproblem 1
x + -0.8636363635 = 0.447675354

Simplifying
x + -0.8636363635 = 0.447675354

Reorder the terms:
-0.8636363635 + x = 0.447675354

Solving
-0.8636363635 + x = 0.447675354

Solving for variable 'x'.

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

Add '0.8636363635' to each side of the equation.
-0.8636363635 + 0.8636363635 + x = 0.447675354 + 0.8636363635

Combine like terms: -0.8636363635 + 0.8636363635 = 0.0000000000
0.0000000000 + x = 0.447675354 + 0.8636363635
x = 0.447675354 + 0.8636363635

Combine like terms: 0.447675354 + 0.8636363635 = 1.3113117175
x = 1.3113117175

Simplifying
x = 1.3113117175

Subproblem 2
x + -0.8636363635 = -0.447675354

Simplifying
x + -0.8636363635 = -0.447675354

Reorder the terms:
-0.8636363635 + x = -0.447675354

Solving
-0.8636363635 + x = -0.447675354

Solving for variable 'x'.

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

Add '0.8636363635' to each side of the equation.
-0.8636363635 + 0.8636363635 + x = -0.447675354 + 0.8636363635

Combine like terms: -0.8636363635 + 0.8636363635 = 0.0000000000
0.0000000000 + x = -0.447675354 + 0.8636363635
x = -0.447675354 + 0.8636363635

Combine like terms: -0.447675354 + 0.8636363635 = 0.4159610095
x = 0.4159610095

Simplifying
x = 0.4159610095

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3113117175, 0.4159610095}