(16+2x)*(16+2x)=228

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Solution for (16+2x)*(16+2x)=228 equation: 


Simplifying
(16 + 2x)(16 + 2x) = 228

Multiply (16 + 2x) * (16 + 2x)
(16(16 + 2x) + 2x * (16 + 2x)) = 228
((16 * 16 + 2x * 16) + 2x * (16 + 2x)) = 228
((256 + 32x) + 2x * (16 + 2x)) = 228
(256 + 32x + (16 * 2x + 2x * 2x)) = 228
(256 + 32x + (32x + 4x2)) = 228

Combine like terms: 32x + 32x = 64x
(256 + 64x + 4x2) = 228

Solving
256 + 64x + 4x2 = 228

Solving for variable 'x'.

Reorder the terms:
256 + -228 + 64x + 4x2 = 228 + -228

Combine like terms: 256 + -228 = 28
28 + 64x + 4x2 = 228 + -228

Combine like terms: 228 + -228 = 0
28 + 64x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + 16x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(7 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
7 + 16x + x2 = 0

Solving
7 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 16x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 16x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 16x + x2 = 0 + -7
16x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
16x + x2 = -7

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 = -7 + 64

Reorder the terms:
64 + 16x + x2 = -7 + 64

Combine like terms: -7 + 64 = 57
64 + 16x + x2 = 57

Factor a perfect square on the left side:
(x + 8)(x + 8) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(x + 8) equal to 7.549834435 and -7.549834435.


Subproblem 1
x + 8 = 7.549834435

Simplifying
x + 8 = 7.549834435

Reorder the terms:
8 + x = 7.549834435

Solving
8 + x = 7.549834435

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 = 7.549834435 + -8

Combine like terms: 8 + -8 = 0
0 + x = 7.549834435 + -8
x = 7.549834435 + -8

Combine like terms: 7.549834435 + -8 = -0.450165565
x = -0.450165565

Simplifying
x = -0.450165565


Subproblem 2
x + 8 = -7.549834435

Simplifying
x + 8 = -7.549834435

Reorder the terms:
8 + x = -7.549834435

Solving
8 + x = -7.549834435

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 = -7.549834435 + -8

Combine like terms: 8 + -8 = 0
0 + x = -7.549834435 + -8
x = -7.549834435 + -8

Combine like terms: -7.549834435 + -8 = -15.549834435
x = -15.549834435

Simplifying
x = -15.549834435


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.450165565, -15.549834435}
Solution
x = {-0.450165565, -15.549834435}

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