p^2+16p+46=0

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Solution for p^2+16p+46=0 equation: 


Simplifying
p2 + 16p + 46 = 0

Reorder the terms:
46 + 16p + p2 = 0

Solving
46 + 16p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '-46' to each side of the equation.
46 + 16p + -46 + p2 = 0 + -46

Reorder the terms:
46 + -46 + 16p + p2 = 0 + -46

Combine like terms: 46 + -46 = 0
0 + 16p + p2 = 0 + -46
16p + p2 = 0 + -46

Combine like terms: 0 + -46 = -46
16p + p2 = -46

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 = -46 + 64

Reorder the terms:
64 + 16p + p2 = -46 + 64

Combine like terms: -46 + 64 = 18
64 + 16p + p2 = 18

Factor a perfect square on the left side:
(p + 8)(p + 8) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(p + 8) equal to 4.242640687 and -4.242640687.


Subproblem 1
p + 8 = 4.242640687

Simplifying
p + 8 = 4.242640687

Reorder the terms:
8 + p = 4.242640687

Solving
8 + p = 4.242640687

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 = 4.242640687 + -8

Combine like terms: 8 + -8 = 0
0 + p = 4.242640687 + -8
p = 4.242640687 + -8

Combine like terms: 4.242640687 + -8 = -3.757359313
p = -3.757359313

Simplifying
p = -3.757359313


Subproblem 2
p + 8 = -4.242640687

Simplifying
p + 8 = -4.242640687

Reorder the terms:
8 + p = -4.242640687

Solving
8 + p = -4.242640687

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 = -4.242640687 + -8

Combine like terms: 8 + -8 = 0
0 + p = -4.242640687 + -8
p = -4.242640687 + -8

Combine like terms: -4.242640687 + -8 = -12.242640687
p = -12.242640687

Simplifying
p = -12.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-3.757359313, -12.242640687}

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