p^2-2p-19=0

Solution for p^2-2p-19=0 equation:

Simplifying
p2 + -2p + -19 = 0

Reorder the terms:
-19 + -2p + p2 = 0

Solving
-19 + -2p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + -2p + 19 + p2 = 0 + 19

Reorder the terms:
-19 + 19 + -2p + p2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -2p + p2 = 0 + 19
-2p + p2 = 0 + 19

Combine like terms: 0 + 19 = 19
-2p + p2 = 19

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 = 19 + 1

Reorder the terms:
1 + -2p + p2 = 19 + 1

Combine like terms: 19 + 1 = 20
1 + -2p + p2 = 20

Factor a perfect square on the left side:
(p + -1)(p + -1) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(p + -1) equal to 4.472135955 and -4.472135955.

Subproblem 1
p + -1 = 4.472135955

Simplifying
p + -1 = 4.472135955

Reorder the terms:
-1 + p = 4.472135955

Solving
-1 + p = 4.472135955

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 = 4.472135955 + 1

Combine like terms: -1 + 1 = 0
0 + p = 4.472135955 + 1
p = 4.472135955 + 1

Combine like terms: 4.472135955 + 1 = 5.472135955
p = 5.472135955

Simplifying
p = 5.472135955

Subproblem 2
p + -1 = -4.472135955

Simplifying
p + -1 = -4.472135955

Reorder the terms:
-1 + p = -4.472135955

Solving
-1 + p = -4.472135955

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 = -4.472135955 + 1

Combine like terms: -1 + 1 = 0
0 + p = -4.472135955 + 1
p = -4.472135955 + 1

Combine like terms: -4.472135955 + 1 = -3.472135955
p = -3.472135955

Simplifying
p = -3.472135955

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {5.472135955, -3.472135955}