x^2-22x+81=0

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Solution for x^2-22x+81=0 equation: 


Simplifying
x2 + -22x + 81 = 0

Reorder the terms:
81 + -22x + x2 = 0

Solving
81 + -22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-81' to each side of the equation.
81 + -22x + -81 + x2 = 0 + -81

Reorder the terms:
81 + -81 + -22x + x2 = 0 + -81

Combine like terms: 81 + -81 = 0
0 + -22x + x2 = 0 + -81
-22x + x2 = 0 + -81

Combine like terms: 0 + -81 = -81
-22x + x2 = -81

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 = -81 + 121

Reorder the terms:
121 + -22x + x2 = -81 + 121

Combine like terms: -81 + 121 = 40
121 + -22x + x2 = 40

Factor a perfect square on the left side:
(x + -11)(x + -11) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + -11) equal to 6.32455532 and -6.32455532.


Subproblem 1
x + -11 = 6.32455532

Simplifying
x + -11 = 6.32455532

Reorder the terms:
-11 + x = 6.32455532

Solving
-11 + x = 6.32455532

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 = 6.32455532 + 11

Combine like terms: -11 + 11 = 0
0 + x = 6.32455532 + 11
x = 6.32455532 + 11

Combine like terms: 6.32455532 + 11 = 17.32455532
x = 17.32455532

Simplifying
x = 17.32455532


Subproblem 2
x + -11 = -6.32455532

Simplifying
x + -11 = -6.32455532

Reorder the terms:
-11 + x = -6.32455532

Solving
-11 + x = -6.32455532

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 = -6.32455532 + 11

Combine like terms: -11 + 11 = 0
0 + x = -6.32455532 + 11
x = -6.32455532 + 11

Combine like terms: -6.32455532 + 11 = 4.67544468
x = 4.67544468

Simplifying
x = 4.67544468


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.32455532, 4.67544468}

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