p^2+6p-41=0

Solution for p^2+6p-41=0 equation:

Simplifying
p2 + 6p + -41 = 0

Reorder the terms:
-41 + 6p + p2 = 0

Solving
-41 + 6p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + 6p + 41 + p2 = 0 + 41

Reorder the terms:
-41 + 41 + 6p + p2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + 6p + p2 = 0 + 41
6p + p2 = 0 + 41

Combine like terms: 0 + 41 = 41
6p + p2 = 41

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 = 41 + 9

Reorder the terms:
9 + 6p + p2 = 41 + 9

Combine like terms: 41 + 9 = 50
9 + 6p + p2 = 50

Factor a perfect square on the left side:
(p + 3)(p + 3) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(p + 3) equal to 7.071067812 and -7.071067812.

Subproblem 1
p + 3 = 7.071067812

Simplifying
p + 3 = 7.071067812

Reorder the terms:
3 + p = 7.071067812

Solving
3 + p = 7.071067812

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 = 7.071067812 + -3

Combine like terms: 3 + -3 = 0
0 + p = 7.071067812 + -3
p = 7.071067812 + -3

Combine like terms: 7.071067812 + -3 = 4.071067812
p = 4.071067812

Simplifying
p = 4.071067812

Subproblem 2
p + 3 = -7.071067812

Simplifying
p + 3 = -7.071067812

Reorder the terms:
3 + p = -7.071067812

Solving
3 + p = -7.071067812

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 = -7.071067812 + -3

Combine like terms: 3 + -3 = 0
0 + p = -7.071067812 + -3
p = -7.071067812 + -3

Combine like terms: -7.071067812 + -3 = -10.071067812
p = -10.071067812

Simplifying
p = -10.071067812

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {4.071067812, -10.071067812}