(40-2x)(46-2x)=1104

Solution for (40-2x)(46-2x)=1104 equation:

Simplifying
(40 + -2x)(46 + -2x) = 1104

Multiply (40 + -2x) * (46 + -2x)
(40(46 + -2x) + -2x * (46 + -2x)) = 1104
((46 * 40 + -2x * 40) + -2x * (46 + -2x)) = 1104
((1840 + -80x) + -2x * (46 + -2x)) = 1104
(1840 + -80x + (46 * -2x + -2x * -2x)) = 1104
(1840 + -80x + (-92x + 4x2)) = 1104

Combine like terms: -80x + -92x = -172x
(1840 + -172x + 4x2) = 1104

Solving
1840 + -172x + 4x2 = 1104

Solving for variable 'x'.

Reorder the terms:
1840 + -1104 + -172x + 4x2 = 1104 + -1104

Combine like terms: 1840 + -1104 = 736
736 + -172x + 4x2 = 1104 + -1104

Combine like terms: 1104 + -1104 = 0
736 + -172x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(184 + -43x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(184 + -43x + x2)' equal to zero and attempt to solve:

Simplifying
184 + -43x + x2 = 0

Solving
184 + -43x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-184' to each side of the equation.
184 + -43x + -184 + x2 = 0 + -184

Reorder the terms:
184 + -184 + -43x + x2 = 0 + -184

Combine like terms: 184 + -184 = 0
0 + -43x + x2 = 0 + -184
-43x + x2 = 0 + -184

Combine like terms: 0 + -184 = -184
-43x + x2 = -184

The x term is -43x.  Take half its coefficient (-21.5).
Square it (462.25) and add it to both sides.

Add '462.25' to each side of the equation.
-43x + 462.25 + x2 = -184 + 462.25

Reorder the terms:
462.25 + -43x + x2 = -184 + 462.25

Combine like terms: -184 + 462.25 = 278.25
462.25 + -43x + x2 = 278.25

Factor a perfect square on the left side:
(x + -21.5)(x + -21.5) = 278.25

Calculate the square root of the right side: 16.680827318

Break this problem into two subproblems by setting 
(x + -21.5) equal to 16.680827318 and -16.680827318.

Subproblem 1
x + -21.5 = 16.680827318

Simplifying
x + -21.5 = 16.680827318

Reorder the terms:
-21.5 + x = 16.680827318

Solving
-21.5 + x = 16.680827318

Solving for variable 'x'.

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

Add '21.5' to each side of the equation.
-21.5 + 21.5 + x = 16.680827318 + 21.5

Combine like terms: -21.5 + 21.5 = 0.0
0.0 + x = 16.680827318 + 21.5
x = 16.680827318 + 21.5

Combine like terms: 16.680827318 + 21.5 = 38.180827318
x = 38.180827318

Simplifying
x = 38.180827318

Subproblem 2
x + -21.5 = -16.680827318

Simplifying
x + -21.5 = -16.680827318

Reorder the terms:
-21.5 + x = -16.680827318

Solving
-21.5 + x = -16.680827318

Solving for variable 'x'.

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

Add '21.5' to each side of the equation.
-21.5 + 21.5 + x = -16.680827318 + 21.5

Combine like terms: -21.5 + 21.5 = 0.0
0.0 + x = -16.680827318 + 21.5
x = -16.680827318 + 21.5

Combine like terms: -16.680827318 + 21.5 = 4.819172682
x = 4.819172682

Simplifying
x = 4.819172682

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {38.180827318, 4.819172682}
Solution
x = {38.180827318, 4.819172682}