p^2-4p-1=0

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

Simplifying
p2 + -4p + -1 = 0

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

Solving
-1 + -4p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4p + 1 + p2 = 0 + 1

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

Combine like terms: -1 + 1 = 0
0 + -4p + p2 = 0 + 1
-4p + p2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4p + p2 = 1

The p term is -4p.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4p + 4 + p2 = 1 + 4

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

Combine like terms: 1 + 4 = 5
4 + -4p + p2 = 5

Factor a perfect square on the left side:
(p + -2)(p + -2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(p + -2) equal to 2.236067978 and -2.236067978.

Subproblem 1
p + -2 = 2.236067978

Simplifying
p + -2 = 2.236067978

Reorder the terms:
-2 + p = 2.236067978

Solving
-2 + p = 2.236067978

Solving for variable 'p'.

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

Add '2' to each side of the equation.
-2 + 2 + p = 2.236067978 + 2

Combine like terms: -2 + 2 = 0
0 + p = 2.236067978 + 2
p = 2.236067978 + 2

Combine like terms: 2.236067978 + 2 = 4.236067978
p = 4.236067978

Simplifying
p = 4.236067978

Subproblem 2
p + -2 = -2.236067978

Simplifying
p + -2 = -2.236067978

Reorder the terms:
-2 + p = -2.236067978

Solving
-2 + p = -2.236067978

Solving for variable 'p'.

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

Add '2' to each side of the equation.
-2 + 2 + p = -2.236067978 + 2

Combine like terms: -2 + 2 = 0
0 + p = -2.236067978 + 2
p = -2.236067978 + 2

Combine like terms: -2.236067978 + 2 = -0.236067978
p = -0.236067978

Simplifying
p = -0.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {4.236067978, -0.236067978}