0=p^2+6p-1

Solution for 0=p^2+6p-1 equation:

Simplifying
0 = p2 + 6p + -1

Reorder the terms:
0 = -1 + 6p + p2

Solving
0 = -1 + 6p + p2

Solving for variable 'p'.

Combine like terms: 0 + 1 = 1
1 + -6p + -1p2 = -1 + 6p + p2 + 1 + -6p + -1p2

Reorder the terms:
1 + -6p + -1p2 = -1 + 1 + 6p + -6p + p2 + -1p2

Combine like terms: -1 + 1 = 0
1 + -6p + -1p2 = 0 + 6p + -6p + p2 + -1p2
1 + -6p + -1p2 = 6p + -6p + p2 + -1p2

Combine like terms: 6p + -6p = 0
1 + -6p + -1p2 = 0 + p2 + -1p2
1 + -6p + -1p2 = p2 + -1p2

Combine like terms: p2 + -1p2 = 0
1 + -6p + -1p2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + 6p + p2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 6p + 1 + p2 = 0 + 1

Reorder the terms:
-1 + 1 + 6p + p2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 6p + p2 = 0 + 1
6p + p2 = 0 + 1

Combine like terms: 0 + 1 = 1
6p + p2 = 1

The p term is 6p.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6p + 9 + p2 = 1 + 9

Reorder the terms:
9 + 6p + p2 = 1 + 9

Combine like terms: 1 + 9 = 10
9 + 6p + p2 = 10

Factor a perfect square on the left side:
(p + 3)(p + 3) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(p + 3) equal to 3.16227766 and -3.16227766.

Subproblem 1
p + 3 = 3.16227766

Simplifying
p + 3 = 3.16227766

Reorder the terms:
3 + p = 3.16227766

Solving
3 + p = 3.16227766

Solving for variable 'p'.

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

Add '-3' to each side of the equation.
3 + -3 + p = 3.16227766 + -3

Combine like terms: 3 + -3 = 0
0 + p = 3.16227766 + -3
p = 3.16227766 + -3

Combine like terms: 3.16227766 + -3 = 0.16227766
p = 0.16227766

Simplifying
p = 0.16227766

Subproblem 2
p + 3 = -3.16227766

Simplifying
p + 3 = -3.16227766

Reorder the terms:
3 + p = -3.16227766

Solving
3 + p = -3.16227766

Solving for variable 'p'.

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

Add '-3' to each side of the equation.
3 + -3 + p = -3.16227766 + -3

Combine like terms: 3 + -3 = 0
0 + p = -3.16227766 + -3
p = -3.16227766 + -3

Combine like terms: -3.16227766 + -3 = -6.16227766
p = -6.16227766

Simplifying
p = -6.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.16227766, -6.16227766}