(14+2x)(18+2x)=228

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Solution for (14+2x)(18+2x)=228 equation: 


Simplifying
(14 + 2x)(18 + 2x) = 228

Multiply (14 + 2x) * (18 + 2x)
(14(18 + 2x) + 2x * (18 + 2x)) = 228
((18 * 14 + 2x * 14) + 2x * (18 + 2x)) = 228
((252 + 28x) + 2x * (18 + 2x)) = 228
(252 + 28x + (18 * 2x + 2x * 2x)) = 228
(252 + 28x + (36x + 4x2)) = 228

Combine like terms: 28x + 36x = 64x
(252 + 64x + 4x2) = 228

Solving
252 + 64x + 4x2 = 228

Solving for variable 'x'.

Reorder the terms:
252 + -228 + 64x + 4x2 = 228 + -228

Combine like terms: 252 + -228 = 24
24 + 64x + 4x2 = 228 + -228

Combine like terms: 228 + -228 = 0
24 + 64x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + 16x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(6 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
6 + 16x + x2 = 0

Solving
6 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 16x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 16x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 16x + x2 = 0 + -6
16x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
16x + x2 = -6

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -6 + 64

Reorder the terms:
64 + 16x + x2 = -6 + 64

Combine like terms: -6 + 64 = 58
64 + 16x + x2 = 58

Factor a perfect square on the left side:
(x + 8)(x + 8) = 58

Calculate the square root of the right side: 7.615773106

Break this problem into two subproblems by setting 
(x + 8) equal to 7.615773106 and -7.615773106.


Subproblem 1
x + 8 = 7.615773106

Simplifying
x + 8 = 7.615773106

Reorder the terms:
8 + x = 7.615773106

Solving
8 + x = 7.615773106

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 7.615773106 + -8

Combine like terms: 8 + -8 = 0
0 + x = 7.615773106 + -8
x = 7.615773106 + -8

Combine like terms: 7.615773106 + -8 = -0.384226894
x = -0.384226894

Simplifying
x = -0.384226894


Subproblem 2
x + 8 = -7.615773106

Simplifying
x + 8 = -7.615773106

Reorder the terms:
8 + x = -7.615773106

Solving
8 + x = -7.615773106

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -7.615773106 + -8

Combine like terms: 8 + -8 = 0
0 + x = -7.615773106 + -8
x = -7.615773106 + -8

Combine like terms: -7.615773106 + -8 = -15.615773106
x = -15.615773106

Simplifying
x = -15.615773106


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.384226894, -15.615773106}
Solution
x = {-0.384226894, -15.615773106}

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