p^2-4=-2p

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

Simplifying
p2 + -4 = -2p

Reorder the terms:
-4 + p2 = -2p

Solving
-4 + p2 = -2p

Solving for variable 'p'.

Reorder the terms:
-4 + 2p + p2 = -2p + 2p

Combine like terms: -2p + 2p = 0
-4 + 2p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 2p + 4 + p2 = 0 + 4

Reorder the terms:
-4 + 4 + 2p + p2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 2p + p2 = 0 + 4
2p + p2 = 0 + 4

Combine like terms: 0 + 4 = 4
2p + p2 = 4

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 = 4 + 1

Reorder the terms:
1 + 2p + p2 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + 2p + p2 = 5

Factor a perfect square on the left side:
(p + 1)(p + 1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(p + 1) equal to 2.236067978 and -2.236067978.

Subproblem 1
p + 1 = 2.236067978

Simplifying
p + 1 = 2.236067978

Reorder the terms:
1 + p = 2.236067978

Solving
1 + p = 2.236067978

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 = 2.236067978 + -1

Combine like terms: 1 + -1 = 0
0 + p = 2.236067978 + -1
p = 2.236067978 + -1

Combine like terms: 2.236067978 + -1 = 1.236067978
p = 1.236067978

Simplifying
p = 1.236067978

Subproblem 2
p + 1 = -2.236067978

Simplifying
p + 1 = -2.236067978

Reorder the terms:
1 + p = -2.236067978

Solving
1 + p = -2.236067978

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 = -2.236067978 + -1

Combine like terms: 1 + -1 = 0
0 + p = -2.236067978 + -1
p = -2.236067978 + -1

Combine like terms: -2.236067978 + -1 = -3.236067978
p = -3.236067978

Simplifying
p = -3.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.236067978, -3.236067978}