X^2+12X+1=0

Solution for X^2+12X+1=0 equation:

Simplifying
X2 + 12X + 1 = 0

Reorder the terms:
1 + 12X + X2 = 0

Solving
1 + 12X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 12X + -1 + X2 = 0 + -1

Reorder the terms:
1 + -1 + 12X + X2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 12X + X2 = 0 + -1
12X + X2 = 0 + -1

Combine like terms: 0 + -1 = -1
12X + X2 = -1

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

Add '36' to each side of the equation.
12X + 36 + X2 = -1 + 36

Reorder the terms:
36 + 12X + X2 = -1 + 36

Combine like terms: -1 + 36 = 35
36 + 12X + X2 = 35

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

Calculate the square root of the right side: 5.916079783

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

Subproblem 1
X + 6 = 5.916079783

Simplifying
X + 6 = 5.916079783

Reorder the terms:
6 + X = 5.916079783

Solving
6 + X = 5.916079783

Solving for variable 'X'.

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

Add '-6' to each side of the equation.
6 + -6 + X = 5.916079783 + -6

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

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

Simplifying
X = -0.083920217

Subproblem 2
X + 6 = -5.916079783

Simplifying
X + 6 = -5.916079783

Reorder the terms:
6 + X = -5.916079783

Solving
6 + X = -5.916079783

Solving for variable 'X'.

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

Add '-6' to each side of the equation.
6 + -6 + X = -5.916079783 + -6

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

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

Simplifying
X = -11.916079783

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