x^2-23x+6=0

Solution for x^2-23x+6=0 equation:

Simplifying
x2 + -23x + 6 = 0

Reorder the terms:
6 + -23x + x2 = 0

Solving
6 + -23x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -23x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -23x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -23x + x2 = 0 + -6
-23x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-23x + x2 = -6

The x term is -23x.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23x + 132.25 + x2 = -6 + 132.25

Reorder the terms:
132.25 + -23x + x2 = -6 + 132.25

Combine like terms: -6 + 132.25 = 126.25
132.25 + -23x + x2 = 126.25

Factor a perfect square on the left side:
(x + -11.5)(x + -11.5) = 126.25

Calculate the square root of the right side: 11.236102527

Break this problem into two subproblems by setting 
(x + -11.5) equal to 11.236102527 and -11.236102527.

Subproblem 1
x + -11.5 = 11.236102527

Simplifying
x + -11.5 = 11.236102527

Reorder the terms:
-11.5 + x = 11.236102527

Solving
-11.5 + x = 11.236102527

Solving for variable 'x'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + x = 11.236102527 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = 11.236102527 + 11.5
x = 11.236102527 + 11.5

Combine like terms: 11.236102527 + 11.5 = 22.736102527
x = 22.736102527

Simplifying
x = 22.736102527

Subproblem 2
x + -11.5 = -11.236102527

Simplifying
x + -11.5 = -11.236102527

Reorder the terms:
-11.5 + x = -11.236102527

Solving
-11.5 + x = -11.236102527

Solving for variable 'x'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + x = -11.236102527 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = -11.236102527 + 11.5
x = -11.236102527 + 11.5

Combine like terms: -11.236102527 + 11.5 = 0.263897473
x = 0.263897473

Simplifying
x = 0.263897473

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.736102527, 0.263897473}