p^2-2p-26=0

Solution for p^2-2p-26=0 equation:

Simplifying
p2 + -2p + -26 = 0

Reorder the terms:
-26 + -2p + p2 = 0

Solving
-26 + -2p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + -2p + 26 + p2 = 0 + 26

Reorder the terms:
-26 + 26 + -2p + p2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -2p + p2 = 0 + 26
-2p + p2 = 0 + 26

Combine like terms: 0 + 26 = 26
-2p + p2 = 26

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 = 26 + 1

Reorder the terms:
1 + -2p + p2 = 26 + 1

Combine like terms: 26 + 1 = 27
1 + -2p + p2 = 27

Factor a perfect square on the left side:
(p + -1)(p + -1) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(p + -1) equal to 5.196152423 and -5.196152423.

Subproblem 1
p + -1 = 5.196152423

Simplifying
p + -1 = 5.196152423

Reorder the terms:
-1 + p = 5.196152423

Solving
-1 + p = 5.196152423

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 = 5.196152423 + 1

Combine like terms: -1 + 1 = 0
0 + p = 5.196152423 + 1
p = 5.196152423 + 1

Combine like terms: 5.196152423 + 1 = 6.196152423
p = 6.196152423

Simplifying
p = 6.196152423

Subproblem 2
p + -1 = -5.196152423

Simplifying
p + -1 = -5.196152423

Reorder the terms:
-1 + p = -5.196152423

Solving
-1 + p = -5.196152423

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 = -5.196152423 + 1

Combine like terms: -1 + 1 = 0
0 + p = -5.196152423 + 1
p = -5.196152423 + 1

Combine like terms: -5.196152423 + 1 = -4.196152423
p = -4.196152423

Simplifying
p = -4.196152423

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {6.196152423, -4.196152423}