(x+2)(2x+2)=130

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Solution for (x+2)(2x+2)=130 equation: 


Simplifying
(x + 2)(2x + 2) = 130

Reorder the terms:
(2 + x)(2x + 2) = 130

Reorder the terms:
(2 + x)(2 + 2x) = 130

Multiply (2 + x) * (2 + 2x)
(2(2 + 2x) + x(2 + 2x)) = 130
((2 * 2 + 2x * 2) + x(2 + 2x)) = 130
((4 + 4x) + x(2 + 2x)) = 130
(4 + 4x + (2 * x + 2x * x)) = 130
(4 + 4x + (2x + 2x2)) = 130

Combine like terms: 4x + 2x = 6x
(4 + 6x + 2x2) = 130

Solving
4 + 6x + 2x2 = 130

Solving for variable 'x'.

Reorder the terms:
4 + -130 + 6x + 2x2 = 130 + -130

Combine like terms: 4 + -130 = -126
-126 + 6x + 2x2 = 130 + -130

Combine like terms: 130 + -130 = 0
-126 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-63 + 3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-63 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-63 + 3x + x2 = 0

Solving
-63 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '63' to each side of the equation.
-63 + 3x + 63 + x2 = 0 + 63

Reorder the terms:
-63 + 63 + 3x + x2 = 0 + 63

Combine like terms: -63 + 63 = 0
0 + 3x + x2 = 0 + 63
3x + x2 = 0 + 63

Combine like terms: 0 + 63 = 63
3x + x2 = 63

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 63 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 63 + 2.25

Combine like terms: 63 + 2.25 = 65.25
2.25 + 3x + x2 = 65.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 65.25

Calculate the square root of the right side: 8.077747211

Break this problem into two subproblems by setting 
(x + 1.5) equal to 8.077747211 and -8.077747211.


Subproblem 1
x + 1.5 = 8.077747211

Simplifying
x + 1.5 = 8.077747211

Reorder the terms:
1.5 + x = 8.077747211

Solving
1.5 + x = 8.077747211

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 8.077747211 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 8.077747211 + -1.5
x = 8.077747211 + -1.5

Combine like terms: 8.077747211 + -1.5 = 6.577747211
x = 6.577747211

Simplifying
x = 6.577747211


Subproblem 2
x + 1.5 = -8.077747211

Simplifying
x + 1.5 = -8.077747211

Reorder the terms:
1.5 + x = -8.077747211

Solving
1.5 + x = -8.077747211

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -8.077747211 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -8.077747211 + -1.5
x = -8.077747211 + -1.5

Combine like terms: -8.077747211 + -1.5 = -9.577747211
x = -9.577747211

Simplifying
x = -9.577747211


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.577747211, -9.577747211}
Solution
x = {6.577747211, -9.577747211}

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