p^2+16p+64=3

Solution for p^2+16p+64=3 equation:

Simplifying
p2 + 16p + 64 = 3

Reorder the terms:
64 + 16p + p2 = 3

Solving
64 + 16p + p2 = 3

Solving for variable 'p'.

Reorder the terms:
64 + -3 + 16p + p2 = 3 + -3

Combine like terms: 64 + -3 = 61
61 + 16p + p2 = 3 + -3

Combine like terms: 3 + -3 = 0
61 + 16p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-61' to each side of the equation.
61 + 16p + -61 + p2 = 0 + -61

Reorder the terms:
61 + -61 + 16p + p2 = 0 + -61

Combine like terms: 61 + -61 = 0
0 + 16p + p2 = 0 + -61
16p + p2 = 0 + -61

Combine like terms: 0 + -61 = -61
16p + p2 = -61

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 = -61 + 64

Reorder the terms:
64 + 16p + p2 = -61 + 64

Combine like terms: -61 + 64 = 3
64 + 16p + p2 = 3

Factor a perfect square on the left side:
(p + 8)(p + 8) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(p + 8) equal to 1.732050808 and -1.732050808.

Subproblem 1
p + 8 = 1.732050808

Simplifying
p + 8 = 1.732050808

Reorder the terms:
8 + p = 1.732050808

Solving
8 + p = 1.732050808

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 = 1.732050808 + -8

Combine like terms: 8 + -8 = 0
0 + p = 1.732050808 + -8
p = 1.732050808 + -8

Combine like terms: 1.732050808 + -8 = -6.267949192
p = -6.267949192

Simplifying
p = -6.267949192

Subproblem 2
p + 8 = -1.732050808

Simplifying
p + 8 = -1.732050808

Reorder the terms:
8 + p = -1.732050808

Solving
8 + p = -1.732050808

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 = -1.732050808 + -8

Combine like terms: 8 + -8 = 0
0 + p = -1.732050808 + -8
p = -1.732050808 + -8

Combine like terms: -1.732050808 + -8 = -9.732050808
p = -9.732050808

Simplifying
p = -9.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-6.267949192, -9.732050808}