x^2-22x+23=0

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Solution for x^2-22x+23=0 equation: 


Simplifying
x2 + -22x + 23 = 0

Reorder the terms:
23 + -22x + x2 = 0

Solving
23 + -22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-23' to each side of the equation.
23 + -22x + -23 + x2 = 0 + -23

Reorder the terms:
23 + -23 + -22x + x2 = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -22x + x2 = 0 + -23
-22x + x2 = 0 + -23

Combine like terms: 0 + -23 = -23
-22x + x2 = -23

The x term is -22x.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22x + 121 + x2 = -23 + 121

Reorder the terms:
121 + -22x + x2 = -23 + 121

Combine like terms: -23 + 121 = 98
121 + -22x + x2 = 98

Factor a perfect square on the left side:
(x + -11)(x + -11) = 98

Calculate the square root of the right side: 9.899494937

Break this problem into two subproblems by setting 
(x + -11) equal to 9.899494937 and -9.899494937.


Subproblem 1
x + -11 = 9.899494937

Simplifying
x + -11 = 9.899494937

Reorder the terms:
-11 + x = 9.899494937

Solving
-11 + x = 9.899494937

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = 9.899494937 + 11

Combine like terms: -11 + 11 = 0
0 + x = 9.899494937 + 11
x = 9.899494937 + 11

Combine like terms: 9.899494937 + 11 = 20.899494937
x = 20.899494937

Simplifying
x = 20.899494937


Subproblem 2
x + -11 = -9.899494937

Simplifying
x + -11 = -9.899494937

Reorder the terms:
-11 + x = -9.899494937

Solving
-11 + x = -9.899494937

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = -9.899494937 + 11

Combine like terms: -11 + 11 = 0
0 + x = -9.899494937 + 11
x = -9.899494937 + 11

Combine like terms: -9.899494937 + 11 = 1.100505063
x = 1.100505063

Simplifying
x = 1.100505063


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.899494937, 1.100505063}

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