p^2-8p-11=0

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Solution for p^2-8p-11=0 equation: 


Simplifying
p2 + -8p + -11 = 0

Reorder the terms:
-11 + -8p + p2 = 0

Solving
-11 + -8p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -8p + 11 + p2 = 0 + 11

Reorder the terms:
-11 + 11 + -8p + p2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -8p + p2 = 0 + 11
-8p + p2 = 0 + 11

Combine like terms: 0 + 11 = 11
-8p + p2 = 11

The p term is -8p.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8p + 16 + p2 = 11 + 16

Reorder the terms:
16 + -8p + p2 = 11 + 16

Combine like terms: 11 + 16 = 27
16 + -8p + p2 = 27

Factor a perfect square on the left side:
(p + -4)(p + -4) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(p + -4) equal to 5.196152423 and -5.196152423.


Subproblem 1
p + -4 = 5.196152423

Simplifying
p + -4 = 5.196152423

Reorder the terms:
-4 + p = 5.196152423

Solving
-4 + p = 5.196152423

Solving for variable 'p'.

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

Add '4' to each side of the equation.
-4 + 4 + p = 5.196152423 + 4

Combine like terms: -4 + 4 = 0
0 + p = 5.196152423 + 4
p = 5.196152423 + 4

Combine like terms: 5.196152423 + 4 = 9.196152423
p = 9.196152423

Simplifying
p = 9.196152423


Subproblem 2
p + -4 = -5.196152423

Simplifying
p + -4 = -5.196152423

Reorder the terms:
-4 + p = -5.196152423

Solving
-4 + p = -5.196152423

Solving for variable 'p'.

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

Add '4' to each side of the equation.
-4 + 4 + p = -5.196152423 + 4

Combine like terms: -4 + 4 = 0
0 + p = -5.196152423 + 4
p = -5.196152423 + 4

Combine like terms: -5.196152423 + 4 = -1.196152423
p = -1.196152423

Simplifying
p = -1.196152423


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {9.196152423, -1.196152423}

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