(20-2x)(8-2x)=88

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Solution for (20-2x)(8-2x)=88 equation: 


Simplifying
(20 + -2x)(8 + -2x) = 88

Multiply (20 + -2x) * (8 + -2x)
(20(8 + -2x) + -2x * (8 + -2x)) = 88
((8 * 20 + -2x * 20) + -2x * (8 + -2x)) = 88
((160 + -40x) + -2x * (8 + -2x)) = 88
(160 + -40x + (8 * -2x + -2x * -2x)) = 88
(160 + -40x + (-16x + 4x2)) = 88

Combine like terms: -40x + -16x = -56x
(160 + -56x + 4x2) = 88

Solving
160 + -56x + 4x2 = 88

Solving for variable 'x'.

Reorder the terms:
160 + -88 + -56x + 4x2 = 88 + -88

Combine like terms: 160 + -88 = 72
72 + -56x + 4x2 = 88 + -88

Combine like terms: 88 + -88 = 0
72 + -56x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(18 + -14x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(18 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
18 + -14x + x2 = 0

Solving
18 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -14x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + -14x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -14x + x2 = 0 + -18
-14x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-14x + x2 = -18

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 = -18 + 49

Reorder the terms:
49 + -14x + x2 = -18 + 49

Combine like terms: -18 + 49 = 31
49 + -14x + x2 = 31

Factor a perfect square on the left side:
(x + -7)(x + -7) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(x + -7) equal to 5.567764363 and -5.567764363.


Subproblem 1
x + -7 = 5.567764363

Simplifying
x + -7 = 5.567764363

Reorder the terms:
-7 + x = 5.567764363

Solving
-7 + x = 5.567764363

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 = 5.567764363 + 7

Combine like terms: -7 + 7 = 0
0 + x = 5.567764363 + 7
x = 5.567764363 + 7

Combine like terms: 5.567764363 + 7 = 12.567764363
x = 12.567764363

Simplifying
x = 12.567764363


Subproblem 2
x + -7 = -5.567764363

Simplifying
x + -7 = -5.567764363

Reorder the terms:
-7 + x = -5.567764363

Solving
-7 + x = -5.567764363

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 = -5.567764363 + 7

Combine like terms: -7 + 7 = 0
0 + x = -5.567764363 + 7
x = -5.567764363 + 7

Combine like terms: -5.567764363 + 7 = 1.432235637
x = 1.432235637

Simplifying
x = 1.432235637


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.567764363, 1.432235637}
Solution
x = {12.567764363, 1.432235637}

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