208=(10+2x)(8+2x)

Solution for 208=(10+2x)(8+2x) equation:

Simplifying
208 = (10 + 2x)(8 + 2x)

Multiply (10 + 2x) * (8 + 2x)
208 = (10(8 + 2x) + 2x * (8 + 2x))
208 = ((8 * 10 + 2x * 10) + 2x * (8 + 2x))
208 = ((80 + 20x) + 2x * (8 + 2x))
208 = (80 + 20x + (8 * 2x + 2x * 2x))
208 = (80 + 20x + (16x + 4x2))

Combine like terms: 20x + 16x = 36x
208 = (80 + 36x + 4x2)

Solving
208 = 80 + 36x + 4x2

Solving for variable 'x'.

Combine like terms: 208 + -80 = 128
128 + -36x + -4x2 = 80 + 36x + 4x2 + -80 + -36x + -4x2

Reorder the terms:
128 + -36x + -4x2 = 80 + -80 + 36x + -36x + 4x2 + -4x2

Combine like terms: 80 + -80 = 0
128 + -36x + -4x2 = 0 + 36x + -36x + 4x2 + -4x2
128 + -36x + -4x2 = 36x + -36x + 4x2 + -4x2

Combine like terms: 36x + -36x = 0
128 + -36x + -4x2 = 0 + 4x2 + -4x2
128 + -36x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
128 + -36x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(32 + -9x + -1x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(32 + -9x + -1x2)' equal to zero and attempt to solve:

Simplifying
32 + -9x + -1x2 = 0

Solving
32 + -9x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-32 + 9x + x2 = 0

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 9x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + 9x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 9x + x2 = 0 + 32
9x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
9x + x2 = 32

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 32 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 32 + 20.25

Combine like terms: 32 + 20.25 = 52.25
20.25 + 9x + x2 = 52.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 52.25

Calculate the square root of the right side: 7.228416147

Break this problem into two subproblems by setting 
(x + 4.5) equal to 7.228416147 and -7.228416147.

Subproblem 1
x + 4.5 = 7.228416147

Simplifying
x + 4.5 = 7.228416147

Reorder the terms:
4.5 + x = 7.228416147

Solving
4.5 + x = 7.228416147

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 7.228416147 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 7.228416147 + -4.5
x = 7.228416147 + -4.5

Combine like terms: 7.228416147 + -4.5 = 2.728416147
x = 2.728416147

Simplifying
x = 2.728416147

Subproblem 2
x + 4.5 = -7.228416147

Simplifying
x + 4.5 = -7.228416147

Reorder the terms:
4.5 + x = -7.228416147

Solving
4.5 + x = -7.228416147

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -7.228416147 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -7.228416147 + -4.5
x = -7.228416147 + -4.5

Combine like terms: -7.228416147 + -4.5 = -11.728416147
x = -11.728416147

Simplifying
x = -11.728416147

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.728416147, -11.728416147}
Solution
x = {2.728416147, -11.728416147}