(12+2x)(16+2x)=1900

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Solution for (12+2x)(16+2x)=1900 equation: 


Simplifying
(12 + 2x)(16 + 2x) = 1900

Multiply (12 + 2x) * (16 + 2x)
(12(16 + 2x) + 2x * (16 + 2x)) = 1900
((16 * 12 + 2x * 12) + 2x * (16 + 2x)) = 1900
((192 + 24x) + 2x * (16 + 2x)) = 1900
(192 + 24x + (16 * 2x + 2x * 2x)) = 1900
(192 + 24x + (32x + 4x2)) = 1900

Combine like terms: 24x + 32x = 56x
(192 + 56x + 4x2) = 1900

Solving
192 + 56x + 4x2 = 1900

Solving for variable 'x'.

Reorder the terms:
192 + -1900 + 56x + 4x2 = 1900 + -1900

Combine like terms: 192 + -1900 = -1708
-1708 + 56x + 4x2 = 1900 + -1900

Combine like terms: 1900 + -1900 = 0
-1708 + 56x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-427 + 14x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-427 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
-427 + 14x + x2 = 0

Solving
-427 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '427' to each side of the equation.
-427 + 14x + 427 + x2 = 0 + 427

Reorder the terms:
-427 + 427 + 14x + x2 = 0 + 427

Combine like terms: -427 + 427 = 0
0 + 14x + x2 = 0 + 427
14x + x2 = 0 + 427

Combine like terms: 0 + 427 = 427
14x + x2 = 427

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 427 + 49

Reorder the terms:
49 + 14x + x2 = 427 + 49

Combine like terms: 427 + 49 = 476
49 + 14x + x2 = 476

Factor a perfect square on the left side:
(x + 7)(x + 7) = 476

Calculate the square root of the right side: 21.817424229

Break this problem into two subproblems by setting 
(x + 7) equal to 21.817424229 and -21.817424229.


Subproblem 1
x + 7 = 21.817424229

Simplifying
x + 7 = 21.817424229

Reorder the terms:
7 + x = 21.817424229

Solving
7 + x = 21.817424229

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 21.817424229 + -7

Combine like terms: 7 + -7 = 0
0 + x = 21.817424229 + -7
x = 21.817424229 + -7

Combine like terms: 21.817424229 + -7 = 14.817424229
x = 14.817424229

Simplifying
x = 14.817424229


Subproblem 2
x + 7 = -21.817424229

Simplifying
x + 7 = -21.817424229

Reorder the terms:
7 + x = -21.817424229

Solving
7 + x = -21.817424229

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -21.817424229 + -7

Combine like terms: 7 + -7 = 0
0 + x = -21.817424229 + -7
x = -21.817424229 + -7

Combine like terms: -21.817424229 + -7 = -28.817424229
x = -28.817424229

Simplifying
x = -28.817424229


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.817424229, -28.817424229}
Solution
x = {14.817424229, -28.817424229}

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