4p^2-8p+1=0

Solution for 4p^2-8p+1=0 equation:

Simplifying
4p2 + -8p + 1 = 0

Reorder the terms:
1 + -8p + 4p2 = 0

Solving
1 + -8p + 4p2 = 0

Solving for variable 'p'.

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

Divide each side by '4'.
0.25 + -2p + p2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -2p + -0.25 + p2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -2p + p2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -2p + p2 = 0 + -0.25
-2p + p2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-2p + p2 = -0.25

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 = -0.25 + 1

Reorder the terms:
1 + -2p + p2 = -0.25 + 1

Combine like terms: -0.25 + 1 = 0.75
1 + -2p + p2 = 0.75

Factor a perfect square on the left side:
(p + -1)(p + -1) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(p + -1) equal to 0.866025404 and -0.866025404.

Subproblem 1
p + -1 = 0.866025404

Simplifying
p + -1 = 0.866025404

Reorder the terms:
-1 + p = 0.866025404

Solving
-1 + p = 0.866025404

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 = 0.866025404 + 1

Combine like terms: -1 + 1 = 0
0 + p = 0.866025404 + 1
p = 0.866025404 + 1

Combine like terms: 0.866025404 + 1 = 1.866025404
p = 1.866025404

Simplifying
p = 1.866025404

Subproblem 2
p + -1 = -0.866025404

Simplifying
p + -1 = -0.866025404

Reorder the terms:
-1 + p = -0.866025404

Solving
-1 + p = -0.866025404

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 = -0.866025404 + 1

Combine like terms: -1 + 1 = 0
0 + p = -0.866025404 + 1
p = -0.866025404 + 1

Combine like terms: -0.866025404 + 1 = 0.133974596
p = 0.133974596

Simplifying
p = 0.133974596

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.866025404, 0.133974596}