p^2+12p-4=0

Solution for p^2+12p-4=0 equation:

Simplifying
p2 + 12p + -4 = 0

Reorder the terms:
-4 + 12p + p2 = 0

Solving
-4 + 12p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 12p + 4 + p2 = 0 + 4

Reorder the terms:
-4 + 4 + 12p + p2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 12p + p2 = 0 + 4
12p + p2 = 0 + 4

Combine like terms: 0 + 4 = 4
12p + p2 = 4

The p term is 12p.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12p + 36 + p2 = 4 + 36

Reorder the terms:
36 + 12p + p2 = 4 + 36

Combine like terms: 4 + 36 = 40
36 + 12p + p2 = 40

Factor a perfect square on the left side:
(p + 6)(p + 6) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(p + 6) equal to 6.32455532 and -6.32455532.

Subproblem 1
p + 6 = 6.32455532

Simplifying
p + 6 = 6.32455532

Reorder the terms:
6 + p = 6.32455532

Solving
6 + p = 6.32455532

Solving for variable 'p'.

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

Add '-6' to each side of the equation.
6 + -6 + p = 6.32455532 + -6

Combine like terms: 6 + -6 = 0
0 + p = 6.32455532 + -6
p = 6.32455532 + -6

Combine like terms: 6.32455532 + -6 = 0.32455532
p = 0.32455532

Simplifying
p = 0.32455532

Subproblem 2
p + 6 = -6.32455532

Simplifying
p + 6 = -6.32455532

Reorder the terms:
6 + p = -6.32455532

Solving
6 + p = -6.32455532

Solving for variable 'p'.

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

Add '-6' to each side of the equation.
6 + -6 + p = -6.32455532 + -6

Combine like terms: 6 + -6 = 0
0 + p = -6.32455532 + -6
p = -6.32455532 + -6

Combine like terms: -6.32455532 + -6 = -12.32455532
p = -12.32455532

Simplifying
p = -12.32455532

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.32455532, -12.32455532}