70=400x(1-x)

Solution for 70=400x(1-x) equation:

Simplifying
70 = 400x(1 + -1x)
70 = (1 * 400x + -1x * 400x)
70 = (400x + -400x2)

Solving
70 = 400x + -400x2

Solving for variable 'x'.

Reorder the terms:
70 + -400x + 400x2 = 400x + -400x + -400x2 + 400x2

Combine like terms: 400x + -400x = 0
70 + -400x + 400x2 = 0 + -400x2 + 400x2
70 + -400x + 400x2 = -400x2 + 400x2

Combine like terms: -400x2 + 400x2 = 0
70 + -400x + 400x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(7 + -40x + 40x2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(7 + -40x + 40x2)' equal to zero and attempt to solve:

Simplifying
7 + -40x + 40x2 = 0

Solving
7 + -40x + 40x2 = 0

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

Divide each side by '40'.
0.175 + -1x + x2 = 0.0

Move the constant term to the right:

Add '-0.175' to each side of the equation.
0.175 + -1x + -0.175 + x2 = 0.0 + -0.175

Reorder the terms:
0.175 + -0.175 + -1x + x2 = 0.0 + -0.175

Combine like terms: 0.175 + -0.175 = 0.000
0.000 + -1x + x2 = 0.0 + -0.175
-1x + x2 = 0.0 + -0.175

Combine like terms: 0.0 + -0.175 = -0.175
-1x + x2 = -0.175

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 = -0.175 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.175 + 0.25

Combine like terms: -0.175 + 0.25 = 0.075
0.25 + -1x + x2 = 0.075

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.075

Calculate the square root of the right side: 0.273861279

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.273861279 and -0.273861279.

Subproblem 1
x + -0.5 = 0.273861279

Simplifying
x + -0.5 = 0.273861279

Reorder the terms:
-0.5 + x = 0.273861279

Solving
-0.5 + x = 0.273861279

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 = 0.273861279 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.273861279 + 0.5
x = 0.273861279 + 0.5

Combine like terms: 0.273861279 + 0.5 = 0.773861279
x = 0.773861279

Simplifying
x = 0.773861279

Subproblem 2
x + -0.5 = -0.273861279

Simplifying
x + -0.5 = -0.273861279

Reorder the terms:
-0.5 + x = -0.273861279

Solving
-0.5 + x = -0.273861279

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 = -0.273861279 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.273861279 + 0.5
x = -0.273861279 + 0.5

Combine like terms: -0.273861279 + 0.5 = 0.226138721
x = 0.226138721

Simplifying
x = 0.226138721

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.773861279, 0.226138721}
Solution
x = {0.773861279, 0.226138721}