-2x(x+6)=-22

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Solution for -2x(x+6)=-22 equation: 


Simplifying
-2x(x + 6) = -22

Reorder the terms:
-2x(6 + x) = -22
(6 * -2x + x * -2x) = -22
(-12x + -2x2) = -22

Solving
-12x + -2x2 = -22

Solving for variable 'x'.

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

Combine like terms: -22 + 22 = 0
22 + -12x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -6x + -1x2) = 0

Ignore the factor 2.

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

Simplifying
11 + -6x + -1x2 = 0

Solving
11 + -6x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-11 + 6x + x2 = 0

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 = 1.472135955
x = 1.472135955

Simplifying
x = 1.472135955


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 = -7.472135955
x = -7.472135955

Simplifying
x = -7.472135955


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

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