p(1-p)=0.0136661808

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Solution for p(1-p)=0.0136661808 equation:


Simplifying
p(1 + -1p) = 0.0136661808
(1 * p + -1p * p) = 0.0136661808
(1p + -1p2) = 0.0136661808

Solving
1p + -1p2 = 0.0136661808

Solving for variable 'p'.

Reorder the terms:
-0.0136661808 + 1p + -1p2 = 0.0136661808 + -0.0136661808

Combine like terms: 0.0136661808 + -0.0136661808 = 0.0000000000
-0.0136661808 + 1p + -1p2 = 0.0000000000

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
0.0136661808 + -1p + p2 = 0.0000000000

Move the constant term to the right:

Add '-0.0136661808' to each side of the equation.
0.0136661808 + -1p + -0.0136661808 + p2 = 0.0000000000 + -0.0136661808

Reorder the terms:
0.0136661808 + -0.0136661808 + -1p + p2 = 0.0000000000 + -0.0136661808

Combine like terms: 0.0136661808 + -0.0136661808 = 0.0000000000
0.0000000000 + -1p + p2 = 0.0000000000 + -0.0136661808
-1p + p2 = 0.0000000000 + -0.0136661808

Combine like terms: 0.0000000000 + -0.0136661808 = -0.0136661808
-1p + p2 = -0.0136661808

The p term is -1p.  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.
-1p + 0.25 + p2 = -0.0136661808 + 0.25

Reorder the terms:
0.25 + -1p + p2 = -0.0136661808 + 0.25

Combine like terms: -0.0136661808 + 0.25 = 0.2363338192
0.25 + -1p + p2 = 0.2363338192

Factor a perfect square on the left side:
(p + -0.5)(p + -0.5) = 0.2363338192

Calculate the square root of the right side: 0.486141769

Break this problem into two subproblems by setting 
(p + -0.5) equal to 0.486141769 and -0.486141769.

Subproblem 1

p + -0.5 = 0.486141769 Simplifying p + -0.5 = 0.486141769 Reorder the terms: -0.5 + p = 0.486141769 Solving -0.5 + p = 0.486141769 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + p = 0.486141769 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = 0.486141769 + 0.5 p = 0.486141769 + 0.5 Combine like terms: 0.486141769 + 0.5 = 0.986141769 p = 0.986141769 Simplifying p = 0.986141769

Subproblem 2

p + -0.5 = -0.486141769 Simplifying p + -0.5 = -0.486141769 Reorder the terms: -0.5 + p = -0.486141769 Solving -0.5 + p = -0.486141769 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + p = -0.486141769 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = -0.486141769 + 0.5 p = -0.486141769 + 0.5 Combine like terms: -0.486141769 + 0.5 = 0.013858231 p = 0.013858231 Simplifying p = 0.013858231

Solution

The solution to the problem is based on the solutions from the subproblems. p = {0.986141769, 0.013858231}

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