p(p+16)=22

Solution for p(p+16)=22 equation:

Simplifying
p(p + 16) = 22

Reorder the terms:
p(16 + p) = 22
(16 * p + p * p) = 22
(16p + p2) = 22

Solving
16p + p2 = 22

Solving for variable 'p'.

Reorder the terms:
-22 + 16p + p2 = 22 + -22

Combine like terms: 22 + -22 = 0
-22 + 16p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + 16p + 22 + p2 = 0 + 22

Reorder the terms:
-22 + 22 + 16p + p2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 16p + p2 = 0 + 22
16p + p2 = 0 + 22

Combine like terms: 0 + 22 = 22
16p + p2 = 22

The p term is 16p.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16p + 64 + p2 = 22 + 64

Reorder the terms:
64 + 16p + p2 = 22 + 64

Combine like terms: 22 + 64 = 86
64 + 16p + p2 = 86

Factor a perfect square on the left side:
(p + 8)(p + 8) = 86

Calculate the square root of the right side: 9.273618495

Break this problem into two subproblems by setting 
(p + 8) equal to 9.273618495 and -9.273618495.

Subproblem 1
p + 8 = 9.273618495

Simplifying
p + 8 = 9.273618495

Reorder the terms:
8 + p = 9.273618495

Solving
8 + p = 9.273618495

Solving for variable 'p'.

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

Add '-8' to each side of the equation.
8 + -8 + p = 9.273618495 + -8

Combine like terms: 8 + -8 = 0
0 + p = 9.273618495 + -8
p = 9.273618495 + -8

Combine like terms: 9.273618495 + -8 = 1.273618495
p = 1.273618495

Simplifying
p = 1.273618495

Subproblem 2
p + 8 = -9.273618495

Simplifying
p + 8 = -9.273618495

Reorder the terms:
8 + p = -9.273618495

Solving
8 + p = -9.273618495

Solving for variable 'p'.

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

Add '-8' to each side of the equation.
8 + -8 + p = -9.273618495 + -8

Combine like terms: 8 + -8 = 0
0 + p = -9.273618495 + -8
p = -9.273618495 + -8

Combine like terms: -9.273618495 + -8 = -17.273618495
p = -17.273618495

Simplifying
p = -17.273618495

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.273618495, -17.273618495}