0=(-2)*(40x-4x)+(50-2x)*(40-4x)

Solution for 0=(-2)*(40x-4x)+(50-2x)*(40-4x) equation:

Simplifying
0 = (-2)(40x + -4x) + (50 + -2x)(40 + -4x)

Combine like terms: 40x + -4x = 36x
0 = -2(36x) + (50 + -2x)(40 + -4x)

Remove parenthesis around (36x)
0 = -2 * 36x + (50 + -2x)(40 + -4x)

Multiply -2 * 36
0 = -72x + (50 + -2x)(40 + -4x)

Multiply (50 + -2x) * (40 + -4x)
0 = -72x + (50(40 + -4x) + -2x * (40 + -4x))
0 = -72x + ((40 * 50 + -4x * 50) + -2x * (40 + -4x))
0 = -72x + ((2000 + -200x) + -2x * (40 + -4x))
0 = -72x + (2000 + -200x + (40 * -2x + -4x * -2x))
0 = -72x + (2000 + -200x + (-80x + 8x2))

Combine like terms: -200x + -80x = -280x
0 = -72x + (2000 + -280x + 8x2)

Reorder the terms:
0 = 2000 + -72x + -280x + 8x2

Combine like terms: -72x + -280x = -352x
0 = 2000 + -352x + 8x2

Solving
0 = 2000 + -352x + 8x2

Solving for variable 'x'.

Combine like terms: 0 + -2000 = -2000
-2000 + 352x + -8x2 = 2000 + -352x + 8x2 + -2000 + 352x + -8x2

Reorder the terms:
-2000 + 352x + -8x2 = 2000 + -2000 + -352x + 352x + 8x2 + -8x2

Combine like terms: 2000 + -2000 = 0
-2000 + 352x + -8x2 = 0 + -352x + 352x + 8x2 + -8x2
-2000 + 352x + -8x2 = -352x + 352x + 8x2 + -8x2

Combine like terms: -352x + 352x = 0
-2000 + 352x + -8x2 = 0 + 8x2 + -8x2
-2000 + 352x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-2000 + 352x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-250 + 44x + -1x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-250 + 44x + -1x2)' equal to zero and attempt to solve:

Simplifying
-250 + 44x + -1x2 = 0

Solving
-250 + 44x + -1x2 = 0

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

Divide each side by '-1'.
250 + -44x + x2 = 0

Move the constant term to the right:

Add '-250' to each side of the equation.
250 + -44x + -250 + x2 = 0 + -250

Reorder the terms:
250 + -250 + -44x + x2 = 0 + -250

Combine like terms: 250 + -250 = 0
0 + -44x + x2 = 0 + -250
-44x + x2 = 0 + -250

Combine like terms: 0 + -250 = -250
-44x + x2 = -250

The x term is -44x.  Take half its coefficient (-22).
Square it (484) and add it to both sides.

Add '484' to each side of the equation.
-44x + 484 + x2 = -250 + 484

Reorder the terms:
484 + -44x + x2 = -250 + 484

Combine like terms: -250 + 484 = 234
484 + -44x + x2 = 234

Factor a perfect square on the left side:
(x + -22)(x + -22) = 234

Calculate the square root of the right side: 15.297058541

Break this problem into two subproblems by setting 
(x + -22) equal to 15.297058541 and -15.297058541.

Subproblem 1
x + -22 = 15.297058541

Simplifying
x + -22 = 15.297058541

Reorder the terms:
-22 + x = 15.297058541

Solving
-22 + x = 15.297058541

Solving for variable 'x'.

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

Add '22' to each side of the equation.
-22 + 22 + x = 15.297058541 + 22

Combine like terms: -22 + 22 = 0
0 + x = 15.297058541 + 22
x = 15.297058541 + 22

Combine like terms: 15.297058541 + 22 = 37.297058541
x = 37.297058541

Simplifying
x = 37.297058541

Subproblem 2
x + -22 = -15.297058541

Simplifying
x + -22 = -15.297058541

Reorder the terms:
-22 + x = -15.297058541

Solving
-22 + x = -15.297058541

Solving for variable 'x'.

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

Add '22' to each side of the equation.
-22 + 22 + x = -15.297058541 + 22

Combine like terms: -22 + 22 = 0
0 + x = -15.297058541 + 22
x = -15.297058541 + 22

Combine like terms: -15.297058541 + 22 = 6.702941459
x = 6.702941459

Simplifying
x = 6.702941459

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {37.297058541, 6.702941459}
Solution
x = {37.297058541, 6.702941459}