(16+2x)*(20+2x)=160

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Solution for (16+2x)*(20+2x)=160 equation: 


Simplifying
(16 + 2x)(20 + 2x) = 160

Multiply (16 + 2x) * (20 + 2x)
(16(20 + 2x) + 2x * (20 + 2x)) = 160
((20 * 16 + 2x * 16) + 2x * (20 + 2x)) = 160
((320 + 32x) + 2x * (20 + 2x)) = 160
(320 + 32x + (20 * 2x + 2x * 2x)) = 160
(320 + 32x + (40x + 4x2)) = 160

Combine like terms: 32x + 40x = 72x
(320 + 72x + 4x2) = 160

Solving
320 + 72x + 4x2 = 160

Solving for variable 'x'.

Reorder the terms:
320 + -160 + 72x + 4x2 = 160 + -160

Combine like terms: 320 + -160 = 160
160 + 72x + 4x2 = 160 + -160

Combine like terms: 160 + -160 = 0
160 + 72x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(40 + 18x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(40 + 18x + x2)' equal to zero and attempt to solve:

Simplifying
40 + 18x + x2 = 0

Solving
40 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + 18x + -40 + x2 = 0 + -40

Reorder the terms:
40 + -40 + 18x + x2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + 18x + x2 = 0 + -40
18x + x2 = 0 + -40

Combine like terms: 0 + -40 = -40
18x + x2 = -40

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = -40 + 81

Reorder the terms:
81 + 18x + x2 = -40 + 81

Combine like terms: -40 + 81 = 41
81 + 18x + x2 = 41

Factor a perfect square on the left side:
(x + 9)(x + 9) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + 9) equal to 6.403124237 and -6.403124237.


Subproblem 1
x + 9 = 6.403124237

Simplifying
x + 9 = 6.403124237

Reorder the terms:
9 + x = 6.403124237

Solving
9 + x = 6.403124237

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = 6.403124237 + -9

Combine like terms: 9 + -9 = 0
0 + x = 6.403124237 + -9
x = 6.403124237 + -9

Combine like terms: 6.403124237 + -9 = -2.596875763
x = -2.596875763

Simplifying
x = -2.596875763


Subproblem 2
x + 9 = -6.403124237

Simplifying
x + 9 = -6.403124237

Reorder the terms:
9 + x = -6.403124237

Solving
9 + x = -6.403124237

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = -6.403124237 + -9

Combine like terms: 9 + -9 = 0
0 + x = -6.403124237 + -9
x = -6.403124237 + -9

Combine like terms: -6.403124237 + -9 = -15.403124237
x = -15.403124237

Simplifying
x = -15.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.596875763, -15.403124237}
Solution
x = {-2.596875763, -15.403124237}

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