1+12l+l^2=0

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

Simplifying
1 + 12l + l2 = 0

Solving
1 + 12l + l2 = 0

Solving for variable 'l'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 12l + -1 + l2 = 0 + -1

Reorder the terms:
1 + -1 + 12l + l2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 12l + l2 = 0 + -1
12l + l2 = 0 + -1

Combine like terms: 0 + -1 = -1
12l + l2 = -1

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

Add '36' to each side of the equation.
12l + 36 + l2 = -1 + 36

Reorder the terms:
36 + 12l + l2 = -1 + 36

Combine like terms: -1 + 36 = 35
36 + 12l + l2 = 35

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

Calculate the square root of the right side: 5.916079783

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

Subproblem 1
l + 6 = 5.916079783

Simplifying
l + 6 = 5.916079783

Reorder the terms:
6 + l = 5.916079783

Solving
6 + l = 5.916079783

Solving for variable 'l'.

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

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

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

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

Simplifying
l = -0.083920217

Subproblem 2
l + 6 = -5.916079783

Simplifying
l + 6 = -5.916079783

Reorder the terms:
6 + l = -5.916079783

Solving
6 + l = -5.916079783

Solving for variable 'l'.

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

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

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

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

Simplifying
l = -11.916079783

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