2x^2-22x+22=0

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


Simplifying
2x2 + -22x + 22 = 0

Reorder the terms:
22 + -22x + 2x2 = 0

Solving
22 + -22x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -11x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(11 + -11x + x2)' equal to zero and attempt to solve:

Simplifying
11 + -11x + x2 = 0

Solving
11 + -11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -11x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + -11x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -11x + x2 = 0 + -11
-11x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
-11x + x2 = -11

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -11 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -11 + 30.25

Combine like terms: -11 + 30.25 = 19.25
30.25 + -11x + x2 = 19.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(x + -5.5) equal to 4.387482194 and -4.387482194.


Subproblem 1
x + -5.5 = 4.387482194

Simplifying
x + -5.5 = 4.387482194

Reorder the terms:
-5.5 + x = 4.387482194

Solving
-5.5 + x = 4.387482194

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 4.387482194 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 4.387482194 + 5.5
x = 4.387482194 + 5.5

Combine like terms: 4.387482194 + 5.5 = 9.887482194
x = 9.887482194

Simplifying
x = 9.887482194


Subproblem 2
x + -5.5 = -4.387482194

Simplifying
x + -5.5 = -4.387482194

Reorder the terms:
-5.5 + x = -4.387482194

Solving
-5.5 + x = -4.387482194

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -4.387482194 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -4.387482194 + 5.5
x = -4.387482194 + 5.5

Combine like terms: -4.387482194 + 5.5 = 1.112517806
x = 1.112517806

Simplifying
x = 1.112517806


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.887482194, 1.112517806}
Solution
x = {9.887482194, 1.112517806}

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