(50-2a)(40-2a)=118

Solution for (50-2a)(40-2a)=118 equation:

Simplifying
(50 + -2a)(40 + -2a) = 118

Multiply (50 + -2a) * (40 + -2a)
(50(40 + -2a) + -2a * (40 + -2a)) = 118
((40 * 50 + -2a * 50) + -2a * (40 + -2a)) = 118
((2000 + -100a) + -2a * (40 + -2a)) = 118
(2000 + -100a + (40 * -2a + -2a * -2a)) = 118
(2000 + -100a + (-80a + 4a2)) = 118

Combine like terms: -100a + -80a = -180a
(2000 + -180a + 4a2) = 118

Solving
2000 + -180a + 4a2 = 118

Solving for variable 'a'.

Reorder the terms:
2000 + -118 + -180a + 4a2 = 118 + -118

Combine like terms: 2000 + -118 = 1882
1882 + -180a + 4a2 = 118 + -118

Combine like terms: 118 + -118 = 0
1882 + -180a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(941 + -90a + 2a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(941 + -90a + 2a2)' equal to zero and attempt to solve:

Simplifying
941 + -90a + 2a2 = 0

Solving
941 + -90a + 2a2 = 0

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

Divide each side by '2'.
470.5 + -45a + a2 = 0

Move the constant term to the right:

Add '-470.5' to each side of the equation.
470.5 + -45a + -470.5 + a2 = 0 + -470.5

Reorder the terms:
470.5 + -470.5 + -45a + a2 = 0 + -470.5

Combine like terms: 470.5 + -470.5 = 0.0
0.0 + -45a + a2 = 0 + -470.5
-45a + a2 = 0 + -470.5

Combine like terms: 0 + -470.5 = -470.5
-45a + a2 = -470.5

The a term is -45a.  Take half its coefficient (-22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
-45a + 506.25 + a2 = -470.5 + 506.25

Reorder the terms:
506.25 + -45a + a2 = -470.5 + 506.25

Combine like terms: -470.5 + 506.25 = 35.75
506.25 + -45a + a2 = 35.75

Factor a perfect square on the left side:
(a + -22.5)(a + -22.5) = 35.75

Calculate the square root of the right side: 5.979130372

Break this problem into two subproblems by setting 
(a + -22.5) equal to 5.979130372 and -5.979130372.

Subproblem 1
a + -22.5 = 5.979130372

Simplifying
a + -22.5 = 5.979130372

Reorder the terms:
-22.5 + a = 5.979130372

Solving
-22.5 + a = 5.979130372

Solving for variable 'a'.

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

Add '22.5' to each side of the equation.
-22.5 + 22.5 + a = 5.979130372 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + a = 5.979130372 + 22.5
a = 5.979130372 + 22.5

Combine like terms: 5.979130372 + 22.5 = 28.479130372
a = 28.479130372

Simplifying
a = 28.479130372

Subproblem 2
a + -22.5 = -5.979130372

Simplifying
a + -22.5 = -5.979130372

Reorder the terms:
-22.5 + a = -5.979130372

Solving
-22.5 + a = -5.979130372

Solving for variable 'a'.

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

Add '22.5' to each side of the equation.
-22.5 + 22.5 + a = -5.979130372 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + a = -5.979130372 + 22.5
a = -5.979130372 + 22.5

Combine like terms: -5.979130372 + 22.5 = 16.520869628
a = 16.520869628

Simplifying
a = 16.520869628

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {28.479130372, 16.520869628}
Solution
a = {28.479130372, 16.520869628}