x^2-22x+121=7

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Solution for x^2-22x+121=7 equation: 


Simplifying
x2 + -22x + 121 = 7

Reorder the terms:
121 + -22x + x2 = 7

Solving
121 + -22x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
121 + -7 + -22x + x2 = 7 + -7

Combine like terms: 121 + -7 = 114
114 + -22x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
114 + -22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-114' to each side of the equation.
114 + -22x + -114 + x2 = 0 + -114

Reorder the terms:
114 + -114 + -22x + x2 = 0 + -114

Combine like terms: 114 + -114 = 0
0 + -22x + x2 = 0 + -114
-22x + x2 = 0 + -114

Combine like terms: 0 + -114 = -114
-22x + x2 = -114

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 = -114 + 121

Reorder the terms:
121 + -22x + x2 = -114 + 121

Combine like terms: -114 + 121 = 7
121 + -22x + x2 = 7

Factor a perfect square on the left side:
(x + -11)(x + -11) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + -11) equal to 2.645751311 and -2.645751311.


Subproblem 1
x + -11 = 2.645751311

Simplifying
x + -11 = 2.645751311

Reorder the terms:
-11 + x = 2.645751311

Solving
-11 + x = 2.645751311

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 = 2.645751311 + 11

Combine like terms: -11 + 11 = 0
0 + x = 2.645751311 + 11
x = 2.645751311 + 11

Combine like terms: 2.645751311 + 11 = 13.645751311
x = 13.645751311

Simplifying
x = 13.645751311


Subproblem 2
x + -11 = -2.645751311

Simplifying
x + -11 = -2.645751311

Reorder the terms:
-11 + x = -2.645751311

Solving
-11 + x = -2.645751311

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 = -2.645751311 + 11

Combine like terms: -11 + 11 = 0
0 + x = -2.645751311 + 11
x = -2.645751311 + 11

Combine like terms: -2.645751311 + 11 = 8.354248689
x = 8.354248689

Simplifying
x = 8.354248689


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.645751311, 8.354248689}

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