p^2+12p=-1

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Solution for p^2+12p=-1 equation: 


Simplifying
p2 + 12p = -1

Reorder the terms:
12p + p2 = -1

Solving
12p + p2 = -1

Solving for variable 'p'.

Reorder the terms:
1 + 12p + p2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + 12p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 12p + -1 + p2 = 0 + -1

Reorder the terms:
1 + -1 + 12p + p2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 12p + p2 = 0 + -1
12p + p2 = 0 + -1

Combine like terms: 0 + -1 = -1
12p + p2 = -1

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 = -1 + 36

Reorder the terms:
36 + 12p + p2 = -1 + 36

Combine like terms: -1 + 36 = 35
36 + 12p + p2 = 35

Factor a perfect square on the left side:
(p + 6)(p + 6) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(p + 6) equal to 5.916079783 and -5.916079783.


Subproblem 1
p + 6 = 5.916079783

Simplifying
p + 6 = 5.916079783

Reorder the terms:
6 + p = 5.916079783

Solving
6 + p = 5.916079783

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 = 5.916079783 + -6

Combine like terms: 6 + -6 = 0
0 + p = 5.916079783 + -6
p = 5.916079783 + -6

Combine like terms: 5.916079783 + -6 = -0.083920217
p = -0.083920217

Simplifying
p = -0.083920217


Subproblem 2
p + 6 = -5.916079783

Simplifying
p + 6 = -5.916079783

Reorder the terms:
6 + p = -5.916079783

Solving
6 + p = -5.916079783

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 = -5.916079783 + -6

Combine like terms: 6 + -6 = 0
0 + p = -5.916079783 + -6
p = -5.916079783 + -6

Combine like terms: -5.916079783 + -6 = -11.916079783
p = -11.916079783

Simplifying
p = -11.916079783


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.083920217, -11.916079783}

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