p^2-8p-32=0

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Solution for p^2-8p-32=0 equation: 


Simplifying
p2 + -8p + -32 = 0

Reorder the terms:
-32 + -8p + p2 = 0

Solving
-32 + -8p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -8p + 32 + p2 = 0 + 32

Reorder the terms:
-32 + 32 + -8p + p2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -8p + p2 = 0 + 32
-8p + p2 = 0 + 32

Combine like terms: 0 + 32 = 32
-8p + p2 = 32

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 = 32 + 16

Reorder the terms:
16 + -8p + p2 = 32 + 16

Combine like terms: 32 + 16 = 48
16 + -8p + p2 = 48

Factor a perfect square on the left side:
(p + -4)(p + -4) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(p + -4) equal to 6.92820323 and -6.92820323.


Subproblem 1
p + -4 = 6.92820323

Simplifying
p + -4 = 6.92820323

Reorder the terms:
-4 + p = 6.92820323

Solving
-4 + p = 6.92820323

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 = 6.92820323 + 4

Combine like terms: -4 + 4 = 0
0 + p = 6.92820323 + 4
p = 6.92820323 + 4

Combine like terms: 6.92820323 + 4 = 10.92820323
p = 10.92820323

Simplifying
p = 10.92820323


Subproblem 2
p + -4 = -6.92820323

Simplifying
p + -4 = -6.92820323

Reorder the terms:
-4 + p = -6.92820323

Solving
-4 + p = -6.92820323

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 = -6.92820323 + 4

Combine like terms: -4 + 4 = 0
0 + p = -6.92820323 + 4
p = -6.92820323 + 4

Combine like terms: -6.92820323 + 4 = -2.92820323
p = -2.92820323

Simplifying
p = -2.92820323


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {10.92820323, -2.92820323}

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