x^2-22x=12544

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Solution for x^2-22x=12544 equation: 


Simplifying
x2 + -22x = 12544

Reorder the terms:
-22x + x2 = 12544

Solving
-22x + x2 = 12544

Solving for variable 'x'.

Reorder the terms:
-12544 + -22x + x2 = 12544 + -12544

Combine like terms: 12544 + -12544 = 0
-12544 + -22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12544' to each side of the equation.
-12544 + -22x + 12544 + x2 = 0 + 12544

Reorder the terms:
-12544 + 12544 + -22x + x2 = 0 + 12544

Combine like terms: -12544 + 12544 = 0
0 + -22x + x2 = 0 + 12544
-22x + x2 = 0 + 12544

Combine like terms: 0 + 12544 = 12544
-22x + x2 = 12544

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 = 12544 + 121

Reorder the terms:
121 + -22x + x2 = 12544 + 121

Combine like terms: 12544 + 121 = 12665
121 + -22x + x2 = 12665

Factor a perfect square on the left side:
(x + -11)(x + -11) = 12665

Calculate the square root of the right side: 112.53888217

Break this problem into two subproblems by setting 
(x + -11) equal to 112.53888217 and -112.53888217.


Subproblem 1
x + -11 = 112.53888217

Simplifying
x + -11 = 112.53888217

Reorder the terms:
-11 + x = 112.53888217

Solving
-11 + x = 112.53888217

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 = 112.53888217 + 11

Combine like terms: -11 + 11 = 0
0 + x = 112.53888217 + 11
x = 112.53888217 + 11

Combine like terms: 112.53888217 + 11 = 123.53888217
x = 123.53888217

Simplifying
x = 123.53888217


Subproblem 2
x + -11 = -112.53888217

Simplifying
x + -11 = -112.53888217

Reorder the terms:
-11 + x = -112.53888217

Solving
-11 + x = -112.53888217

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 = -112.53888217 + 11

Combine like terms: -11 + 11 = 0
0 + x = -112.53888217 + 11
x = -112.53888217 + 11

Combine like terms: -112.53888217 + 11 = -101.53888217
x = -101.53888217

Simplifying
x = -101.53888217


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {123.53888217, -101.53888217}

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