p^2+8p+6=0

Solution for p^2+8p+6=0 equation:

Simplifying
p2 + 8p + 6 = 0

Reorder the terms:
6 + 8p + p2 = 0

Solving
6 + 8p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 8p + -6 + p2 = 0 + -6

Reorder the terms:
6 + -6 + 8p + p2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 8p + p2 = 0 + -6
8p + p2 = 0 + -6

Combine like terms: 0 + -6 = -6
8p + p2 = -6

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 = -6 + 16

Reorder the terms:
16 + 8p + p2 = -6 + 16

Combine like terms: -6 + 16 = 10
16 + 8p + p2 = 10

Factor a perfect square on the left side:
(p + 4)(p + 4) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(p + 4) equal to 3.16227766 and -3.16227766.

Subproblem 1
p + 4 = 3.16227766

Simplifying
p + 4 = 3.16227766

Reorder the terms:
4 + p = 3.16227766

Solving
4 + p = 3.16227766

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 = 3.16227766 + -4

Combine like terms: 4 + -4 = 0
0 + p = 3.16227766 + -4
p = 3.16227766 + -4

Combine like terms: 3.16227766 + -4 = -0.83772234
p = -0.83772234

Simplifying
p = -0.83772234

Subproblem 2
p + 4 = -3.16227766

Simplifying
p + 4 = -3.16227766

Reorder the terms:
4 + p = -3.16227766

Solving
4 + p = -3.16227766

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 = -3.16227766 + -4

Combine like terms: 4 + -4 = 0
0 + p = -3.16227766 + -4
p = -3.16227766 + -4

Combine like terms: -3.16227766 + -4 = -7.16227766
p = -7.16227766

Simplifying
p = -7.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.83772234, -7.16227766}