(12+2x)(10+2x)=104

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Solution for (12+2x)(10+2x)=104 equation: 


Simplifying
(12 + 2x)(10 + 2x) = 104

Multiply (12 + 2x) * (10 + 2x)
(12(10 + 2x) + 2x * (10 + 2x)) = 104
((10 * 12 + 2x * 12) + 2x * (10 + 2x)) = 104
((120 + 24x) + 2x * (10 + 2x)) = 104
(120 + 24x + (10 * 2x + 2x * 2x)) = 104
(120 + 24x + (20x + 4x2)) = 104

Combine like terms: 24x + 20x = 44x
(120 + 44x + 4x2) = 104

Solving
120 + 44x + 4x2 = 104

Solving for variable 'x'.

Reorder the terms:
120 + -104 + 44x + 4x2 = 104 + -104

Combine like terms: 120 + -104 = 16
16 + 44x + 4x2 = 104 + -104

Combine like terms: 104 + -104 = 0
16 + 44x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + 11x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(4 + 11x + x2)' equal to zero and attempt to solve:

Simplifying
4 + 11x + x2 = 0

Solving
4 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 11x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 11x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 11x + x2 = 0 + -4
11x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
11x + x2 = -4

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 = -4 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -4 + 30.25

Combine like terms: -4 + 30.25 = 26.25
30.25 + 11x + x2 = 26.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(x + 5.5) equal to 5.123475383 and -5.123475383.


Subproblem 1
x + 5.5 = 5.123475383

Simplifying
x + 5.5 = 5.123475383

Reorder the terms:
5.5 + x = 5.123475383

Solving
5.5 + x = 5.123475383

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 = 5.123475383 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 5.123475383 + -5.5
x = 5.123475383 + -5.5

Combine like terms: 5.123475383 + -5.5 = -0.376524617
x = -0.376524617

Simplifying
x = -0.376524617


Subproblem 2
x + 5.5 = -5.123475383

Simplifying
x + 5.5 = -5.123475383

Reorder the terms:
5.5 + x = -5.123475383

Solving
5.5 + x = -5.123475383

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 = -5.123475383 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -5.123475383 + -5.5
x = -5.123475383 + -5.5

Combine like terms: -5.123475383 + -5.5 = -10.623475383
x = -10.623475383

Simplifying
x = -10.623475383


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.376524617, -10.623475383}
Solution
x = {-0.376524617, -10.623475383}

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