5=50x(1-x)

Solution for 5=50x(1-x) equation:

Simplifying
5 = 50x(1 + -1x)
5 = (1 * 50x + -1x * 50x)
5 = (50x + -50x2)

Solving
5 = 50x + -50x2

Solving for variable 'x'.

Reorder the terms:
5 + -50x + 50x2 = 50x + -50x + -50x2 + 50x2

Combine like terms: 50x + -50x = 0
5 + -50x + 50x2 = 0 + -50x2 + 50x2
5 + -50x + 50x2 = -50x2 + 50x2

Combine like terms: -50x2 + 50x2 = 0
5 + -50x + 50x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + -10x + 10x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(1 + -10x + 10x2)' equal to zero and attempt to solve:

Simplifying
1 + -10x + 10x2 = 0

Solving
1 + -10x + 10x2 = 0

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

Divide each side by '10'.
0.1 + -1x + x2 = 0.0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + -1x + -0.1 + x2 = 0.0 + -0.1

Reorder the terms:
0.1 + -0.1 + -1x + x2 = 0.0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + -1x + x2 = 0.0 + -0.1
-1x + x2 = 0.0 + -0.1

Combine like terms: 0.0 + -0.1 = -0.1
-1x + x2 = -0.1

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -0.1 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.1 + 0.25

Combine like terms: -0.1 + 0.25 = 0.15
0.25 + -1x + x2 = 0.15

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.15

Calculate the square root of the right side: 0.387298335

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.387298335 and -0.387298335.

Subproblem 1
x + -0.5 = 0.387298335

Simplifying
x + -0.5 = 0.387298335

Reorder the terms:
-0.5 + x = 0.387298335

Solving
-0.5 + x = 0.387298335

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 0.387298335 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.387298335 + 0.5
x = 0.387298335 + 0.5

Combine like terms: 0.387298335 + 0.5 = 0.887298335
x = 0.887298335

Simplifying
x = 0.887298335

Subproblem 2
x + -0.5 = -0.387298335

Simplifying
x + -0.5 = -0.387298335

Reorder the terms:
-0.5 + x = -0.387298335

Solving
-0.5 + x = -0.387298335

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -0.387298335 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.387298335 + 0.5
x = -0.387298335 + 0.5

Combine like terms: -0.387298335 + 0.5 = 0.112701665
x = 0.112701665

Simplifying
x = 0.112701665

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.887298335, 0.112701665}
Solution
x = {0.887298335, 0.112701665}