p^2+16p+11=0

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Solution for p^2+16p+11=0 equation: 


Simplifying
p2 + 16p + 11 = 0

Reorder the terms:
11 + 16p + p2 = 0

Solving
11 + 16p + 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 + 16p + -11 + p2 = 0 + -11

Reorder the terms:
11 + -11 + 16p + p2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 16p + p2 = 0 + -11
16p + p2 = 0 + -11

Combine like terms: 0 + -11 = -11
16p + p2 = -11

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 = -11 + 64

Reorder the terms:
64 + 16p + p2 = -11 + 64

Combine like terms: -11 + 64 = 53
64 + 16p + p2 = 53

Factor a perfect square on the left side:
(p + 8)(p + 8) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(p + 8) equal to 7.280109889 and -7.280109889.


Subproblem 1
p + 8 = 7.280109889

Simplifying
p + 8 = 7.280109889

Reorder the terms:
8 + p = 7.280109889

Solving
8 + p = 7.280109889

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 = 7.280109889 + -8

Combine like terms: 8 + -8 = 0
0 + p = 7.280109889 + -8
p = 7.280109889 + -8

Combine like terms: 7.280109889 + -8 = -0.719890111
p = -0.719890111

Simplifying
p = -0.719890111


Subproblem 2
p + 8 = -7.280109889

Simplifying
p + 8 = -7.280109889

Reorder the terms:
8 + p = -7.280109889

Solving
8 + p = -7.280109889

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 = -7.280109889 + -8

Combine like terms: 8 + -8 = 0
0 + p = -7.280109889 + -8
p = -7.280109889 + -8

Combine like terms: -7.280109889 + -8 = -15.280109889
p = -15.280109889

Simplifying
p = -15.280109889


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.719890111, -15.280109889}

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