x^2-23x+121=0

Solution for x^2-23x+121=0 equation:

Simplifying
x2 + -23x + 121 = 0

Reorder the terms:
121 + -23x + x2 = 0

Solving
121 + -23x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-121' to each side of the equation.
121 + -23x + -121 + x2 = 0 + -121

Reorder the terms:
121 + -121 + -23x + x2 = 0 + -121

Combine like terms: 121 + -121 = 0
0 + -23x + x2 = 0 + -121
-23x + x2 = 0 + -121

Combine like terms: 0 + -121 = -121
-23x + x2 = -121

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 = -121 + 132.25

Reorder the terms:
132.25 + -23x + x2 = -121 + 132.25

Combine like terms: -121 + 132.25 = 11.25
132.25 + -23x + x2 = 11.25

Factor a perfect square on the left side:
(x + -11.5)(x + -11.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + -11.5) equal to 3.354101966 and -3.354101966.

Subproblem 1
x + -11.5 = 3.354101966

Simplifying
x + -11.5 = 3.354101966

Reorder the terms:
-11.5 + x = 3.354101966

Solving
-11.5 + x = 3.354101966

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 = 3.354101966 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = 3.354101966 + 11.5
x = 3.354101966 + 11.5

Combine like terms: 3.354101966 + 11.5 = 14.854101966
x = 14.854101966

Simplifying
x = 14.854101966

Subproblem 2
x + -11.5 = -3.354101966

Simplifying
x + -11.5 = -3.354101966

Reorder the terms:
-11.5 + x = -3.354101966

Solving
-11.5 + x = -3.354101966

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 = -3.354101966 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = -3.354101966 + 11.5
x = -3.354101966 + 11.5

Combine like terms: -3.354101966 + 11.5 = 8.145898034
x = 8.145898034

Simplifying
x = 8.145898034

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.854101966, 8.145898034}