(2x+22)(x-5)=130

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Solution for (2x+22)(x-5)=130 equation: 


Simplifying
(2x + 22)(x + -5) = 130

Reorder the terms:
(22 + 2x)(x + -5) = 130

Reorder the terms:
(22 + 2x)(-5 + x) = 130

Multiply (22 + 2x) * (-5 + x)
(22(-5 + x) + 2x * (-5 + x)) = 130
((-5 * 22 + x * 22) + 2x * (-5 + x)) = 130
((-110 + 22x) + 2x * (-5 + x)) = 130
(-110 + 22x + (-5 * 2x + x * 2x)) = 130
(-110 + 22x + (-10x + 2x2)) = 130

Combine like terms: 22x + -10x = 12x
(-110 + 12x + 2x2) = 130

Solving
-110 + 12x + 2x2 = 130

Solving for variable 'x'.

Reorder the terms:
-110 + -130 + 12x + 2x2 = 130 + -130

Combine like terms: -110 + -130 = -240
-240 + 12x + 2x2 = 130 + -130

Combine like terms: 130 + -130 = 0
-240 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-120 + 6x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-120 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-120 + 6x + x2 = 0

Solving
-120 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + 6x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + 6x + x2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + 6x + x2 = 0 + 120
6x + x2 = 0 + 120

Combine like terms: 0 + 120 = 120
6x + x2 = 120

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 = 120 + 9

Reorder the terms:
9 + 6x + x2 = 120 + 9

Combine like terms: 120 + 9 = 129
9 + 6x + x2 = 129

Factor a perfect square on the left side:
(x + 3)(x + 3) = 129

Calculate the square root of the right side: 11.357816692

Break this problem into two subproblems by setting 
(x + 3) equal to 11.357816692 and -11.357816692.


Subproblem 1
x + 3 = 11.357816692

Simplifying
x + 3 = 11.357816692

Reorder the terms:
3 + x = 11.357816692

Solving
3 + x = 11.357816692

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 = 11.357816692 + -3

Combine like terms: 3 + -3 = 0
0 + x = 11.357816692 + -3
x = 11.357816692 + -3

Combine like terms: 11.357816692 + -3 = 8.357816692
x = 8.357816692

Simplifying
x = 8.357816692


Subproblem 2
x + 3 = -11.357816692

Simplifying
x + 3 = -11.357816692

Reorder the terms:
3 + x = -11.357816692

Solving
3 + x = -11.357816692

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 = -11.357816692 + -3

Combine like terms: 3 + -3 = 0
0 + x = -11.357816692 + -3
x = -11.357816692 + -3

Combine like terms: -11.357816692 + -3 = -14.357816692
x = -14.357816692

Simplifying
x = -14.357816692


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.357816692, -14.357816692}
Solution
x = {8.357816692, -14.357816692}

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