400=x(100-2x)

Solution for 400=x(100-2x) equation:

Simplifying
400 = x(100 + -2x)
400 = (100 * x + -2x * x)
400 = (100x + -2x2)

Solving
400 = 100x + -2x2

Solving for variable 'x'.

Reorder the terms:
400 + -100x + 2x2 = 100x + -100x + -2x2 + 2x2

Combine like terms: 100x + -100x = 0
400 + -100x + 2x2 = 0 + -2x2 + 2x2
400 + -100x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
400 + -100x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(200 + -50x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(200 + -50x + x2)' equal to zero and attempt to solve:

Simplifying
200 + -50x + x2 = 0

Solving
200 + -50x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-200' to each side of the equation.
200 + -50x + -200 + x2 = 0 + -200

Reorder the terms:
200 + -200 + -50x + x2 = 0 + -200

Combine like terms: 200 + -200 = 0
0 + -50x + x2 = 0 + -200
-50x + x2 = 0 + -200

Combine like terms: 0 + -200 = -200
-50x + x2 = -200

The x term is -50x.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50x + 625 + x2 = -200 + 625

Reorder the terms:
625 + -50x + x2 = -200 + 625

Combine like terms: -200 + 625 = 425
625 + -50x + x2 = 425

Factor a perfect square on the left side:
(x + -25)(x + -25) = 425

Calculate the square root of the right side: 20.615528128

Break this problem into two subproblems by setting 
(x + -25) equal to 20.615528128 and -20.615528128.

Subproblem 1
x + -25 = 20.615528128

Simplifying
x + -25 = 20.615528128

Reorder the terms:
-25 + x = 20.615528128

Solving
-25 + x = 20.615528128

Solving for variable 'x'.

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

Add '25' to each side of the equation.
-25 + 25 + x = 20.615528128 + 25

Combine like terms: -25 + 25 = 0
0 + x = 20.615528128 + 25
x = 20.615528128 + 25

Combine like terms: 20.615528128 + 25 = 45.615528128
x = 45.615528128

Simplifying
x = 45.615528128

Subproblem 2
x + -25 = -20.615528128

Simplifying
x + -25 = -20.615528128

Reorder the terms:
-25 + x = -20.615528128

Solving
-25 + x = -20.615528128

Solving for variable 'x'.

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

Add '25' to each side of the equation.
-25 + 25 + x = -20.615528128 + 25

Combine like terms: -25 + 25 = 0
0 + x = -20.615528128 + 25
x = -20.615528128 + 25

Combine like terms: -20.615528128 + 25 = 4.384471872
x = 4.384471872

Simplifying
x = 4.384471872

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {45.615528128, 4.384471872}
Solution
x = {45.615528128, 4.384471872}