2x^2-12x-22=0

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Solution for 2x^2-12x-22=0 equation: 


Simplifying
2x2 + -12x + -22 = 0

Reorder the terms:
-22 + -12x + 2x2 = 0

Solving
-22 + -12x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + -6x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-11 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-11 + -6x + x2 = 0

Solving
-11 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -6x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + -6x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -6x + x2 = 0 + 11
-6x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
-6x + x2 = 11

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 11 + 9

Reorder the terms:
9 + -6x + x2 = 11 + 9

Combine like terms: 11 + 9 = 20
9 + -6x + x2 = 20

Factor a perfect square on the left side:
(x + -3)(x + -3) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x + -3) equal to 4.472135955 and -4.472135955.


Subproblem 1
x + -3 = 4.472135955

Simplifying
x + -3 = 4.472135955

Reorder the terms:
-3 + x = 4.472135955

Solving
-3 + x = 4.472135955

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 4.472135955 + 3

Combine like terms: -3 + 3 = 0
0 + x = 4.472135955 + 3
x = 4.472135955 + 3

Combine like terms: 4.472135955 + 3 = 7.472135955
x = 7.472135955

Simplifying
x = 7.472135955


Subproblem 2
x + -3 = -4.472135955

Simplifying
x + -3 = -4.472135955

Reorder the terms:
-3 + x = -4.472135955

Solving
-3 + x = -4.472135955

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -4.472135955 + 3

Combine like terms: -3 + 3 = 0
0 + x = -4.472135955 + 3
x = -4.472135955 + 3

Combine like terms: -4.472135955 + 3 = -1.472135955
x = -1.472135955

Simplifying
x = -1.472135955


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.472135955, -1.472135955}
Solution
x = {7.472135955, -1.472135955}

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