(12+2x)(10+2x)=600

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Solution for (12+2x)(10+2x)=600 equation: 


Simplifying
(12 + 2x)(10 + 2x) = 600

Multiply (12 + 2x) * (10 + 2x)
(12(10 + 2x) + 2x * (10 + 2x)) = 600
((10 * 12 + 2x * 12) + 2x * (10 + 2x)) = 600
((120 + 24x) + 2x * (10 + 2x)) = 600
(120 + 24x + (10 * 2x + 2x * 2x)) = 600
(120 + 24x + (20x + 4x2)) = 600

Combine like terms: 24x + 20x = 44x
(120 + 44x + 4x2) = 600

Solving
120 + 44x + 4x2 = 600

Solving for variable 'x'.

Reorder the terms:
120 + -600 + 44x + 4x2 = 600 + -600

Combine like terms: 120 + -600 = -480
-480 + 44x + 4x2 = 600 + -600

Combine like terms: 600 + -600 = 0
-480 + 44x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-120 + 11x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-120 + 11x + x2)' equal to zero and attempt to solve:

Simplifying
-120 + 11x + x2 = 0

Solving
-120 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + 11x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + 11x + x2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + 11x + x2 = 0 + 120
11x + x2 = 0 + 120

Combine like terms: 0 + 120 = 120
11x + x2 = 120

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 = 120 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 120 + 30.25

Combine like terms: 120 + 30.25 = 150.25
30.25 + 11x + x2 = 150.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 150.25

Calculate the square root of the right side: 12.257650672

Break this problem into two subproblems by setting 
(x + 5.5) equal to 12.257650672 and -12.257650672.


Subproblem 1
x + 5.5 = 12.257650672

Simplifying
x + 5.5 = 12.257650672

Reorder the terms:
5.5 + x = 12.257650672

Solving
5.5 + x = 12.257650672

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 = 12.257650672 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 12.257650672 + -5.5
x = 12.257650672 + -5.5

Combine like terms: 12.257650672 + -5.5 = 6.757650672
x = 6.757650672

Simplifying
x = 6.757650672


Subproblem 2
x + 5.5 = -12.257650672

Simplifying
x + 5.5 = -12.257650672

Reorder the terms:
5.5 + x = -12.257650672

Solving
5.5 + x = -12.257650672

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 = -12.257650672 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -12.257650672 + -5.5
x = -12.257650672 + -5.5

Combine like terms: -12.257650672 + -5.5 = -17.757650672
x = -17.757650672

Simplifying
x = -17.757650672


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.757650672, -17.757650672}
Solution
x = {6.757650672, -17.757650672}

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