x^2-22x+7=0

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Solution for x^2-22x+7=0 equation: 


Simplifying
x2 + -22x + 7 = 0

Reorder the terms:
7 + -22x + x2 = 0

Solving
7 + -22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -22x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -22x + x2 = 0 + -7

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

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

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 = -7 + 121

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

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

Factor a perfect square on the left side:
(x + -11)(x + -11) = 114

Calculate the square root of the right side: 10.677078252

Break this problem into two subproblems by setting 
(x + -11) equal to 10.677078252 and -10.677078252.


Subproblem 1
x + -11 = 10.677078252

Simplifying
x + -11 = 10.677078252

Reorder the terms:
-11 + x = 10.677078252

Solving
-11 + x = 10.677078252

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 = 10.677078252 + 11

Combine like terms: -11 + 11 = 0
0 + x = 10.677078252 + 11
x = 10.677078252 + 11

Combine like terms: 10.677078252 + 11 = 21.677078252
x = 21.677078252

Simplifying
x = 21.677078252


Subproblem 2
x + -11 = -10.677078252

Simplifying
x + -11 = -10.677078252

Reorder the terms:
-11 + x = -10.677078252

Solving
-11 + x = -10.677078252

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 = -10.677078252 + 11

Combine like terms: -11 + 11 = 0
0 + x = -10.677078252 + 11
x = -10.677078252 + 11

Combine like terms: -10.677078252 + 11 = 0.322921748
x = 0.322921748

Simplifying
x = 0.322921748


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.677078252, 0.322921748}

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