p^2+2p(1-p)=0.5775

Solution for p^2+2p(1-p)=0.5775 equation:

Simplifying
p2 + 2p(1 + -1p) = 0.5775
p2 + (1 * 2p + -1p * 2p) = 0.5775
p2 + (2p + -2p2) = 0.5775

Reorder the terms:
2p + p2 + -2p2 = 0.5775

Combine like terms: p2 + -2p2 = -1p2
2p + -1p2 = 0.5775

Solving
2p + -1p2 = 0.5775

Solving for variable 'p'.

Reorder the terms:
-0.5775 + 2p + -1p2 = 0.5775 + -0.5775

Combine like terms: 0.5775 + -0.5775 = 0.0000
-0.5775 + 2p + -1p2 = 0.0000

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

Divide each side by '-1'.
0.5775 + -2p + p2 = 0.0000

Move the constant term to the right:

Add '-0.5775' to each side of the equation.
0.5775 + -2p + -0.5775 + p2 = 0.0000 + -0.5775

Reorder the terms:
0.5775 + -0.5775 + -2p + p2 = 0.0000 + -0.5775

Combine like terms: 0.5775 + -0.5775 = 0.0000
0.0000 + -2p + p2 = 0.0000 + -0.5775
-2p + p2 = 0.0000 + -0.5775

Combine like terms: 0.0000 + -0.5775 = -0.5775
-2p + p2 = -0.5775

The p term is -2p.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2p + 1 + p2 = -0.5775 + 1

Reorder the terms:
1 + -2p + p2 = -0.5775 + 1

Combine like terms: -0.5775 + 1 = 0.4225
1 + -2p + p2 = 0.4225

Factor a perfect square on the left side:
(p + -1)(p + -1) = 0.4225

Calculate the square root of the right side: 0.65

Break this problem into two subproblems by setting 
(p + -1) equal to 0.65 and -0.65.

Subproblem 1
p + -1 = 0.65

Simplifying
p + -1 = 0.65

Reorder the terms:
-1 + p = 0.65

Solving
-1 + p = 0.65

Solving for variable 'p'.

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

Add '1' to each side of the equation.
-1 + 1 + p = 0.65 + 1

Combine like terms: -1 + 1 = 0
0 + p = 0.65 + 1
p = 0.65 + 1

Combine like terms: 0.65 + 1 = 1.65
p = 1.65

Simplifying
p = 1.65

Subproblem 2
p + -1 = -0.65

Simplifying
p + -1 = -0.65

Reorder the terms:
-1 + p = -0.65

Solving
-1 + p = -0.65

Solving for variable 'p'.

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

Add '1' to each side of the equation.
-1 + 1 + p = -0.65 + 1

Combine like terms: -1 + 1 = 0
0 + p = -0.65 + 1
p = -0.65 + 1

Combine like terms: -0.65 + 1 = 0.35
p = 0.35

Simplifying
p = 0.35

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.65, 0.35}