(50-2x)(30-2x)=200

Solution for (50-2x)(30-2x)=200 equation:

Simplifying
(50 + -2x)(30 + -2x) = 200

Multiply (50 + -2x) * (30 + -2x)
(50(30 + -2x) + -2x * (30 + -2x)) = 200
((30 * 50 + -2x * 50) + -2x * (30 + -2x)) = 200
((1500 + -100x) + -2x * (30 + -2x)) = 200
(1500 + -100x + (30 * -2x + -2x * -2x)) = 200
(1500 + -100x + (-60x + 4x2)) = 200

Combine like terms: -100x + -60x = -160x
(1500 + -160x + 4x2) = 200

Solving
1500 + -160x + 4x2 = 200

Solving for variable 'x'.

Reorder the terms:
1500 + -200 + -160x + 4x2 = 200 + -200

Combine like terms: 1500 + -200 = 1300
1300 + -160x + 4x2 = 200 + -200

Combine like terms: 200 + -200 = 0
1300 + -160x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(325 + -40x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(325 + -40x + x2)' equal to zero and attempt to solve:

Simplifying
325 + -40x + x2 = 0

Solving
325 + -40x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-325' to each side of the equation.
325 + -40x + -325 + x2 = 0 + -325

Reorder the terms:
325 + -325 + -40x + x2 = 0 + -325

Combine like terms: 325 + -325 = 0
0 + -40x + x2 = 0 + -325
-40x + x2 = 0 + -325

Combine like terms: 0 + -325 = -325
-40x + x2 = -325

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = -325 + 400

Reorder the terms:
400 + -40x + x2 = -325 + 400

Combine like terms: -325 + 400 = 75
400 + -40x + x2 = 75

Factor a perfect square on the left side:
(x + -20)(x + -20) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(x + -20) equal to 8.660254038 and -8.660254038.

Subproblem 1
x + -20 = 8.660254038

Simplifying
x + -20 = 8.660254038

Reorder the terms:
-20 + x = 8.660254038

Solving
-20 + x = 8.660254038

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = 8.660254038 + 20

Combine like terms: -20 + 20 = 0
0 + x = 8.660254038 + 20
x = 8.660254038 + 20

Combine like terms: 8.660254038 + 20 = 28.660254038
x = 28.660254038

Simplifying
x = 28.660254038

Subproblem 2
x + -20 = -8.660254038

Simplifying
x + -20 = -8.660254038

Reorder the terms:
-20 + x = -8.660254038

Solving
-20 + x = -8.660254038

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = -8.660254038 + 20

Combine like terms: -20 + 20 = 0
0 + x = -8.660254038 + 20
x = -8.660254038 + 20

Combine like terms: -8.660254038 + 20 = 11.339745962
x = 11.339745962

Simplifying
x = 11.339745962

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {28.660254038, 11.339745962}
Solution
x = {28.660254038, 11.339745962}