-x^2-12x-13=0

Solution for -x^2-12x-13=0 equation:

Simplifying
-1x2 + -12x + -13 = 0

Reorder the terms:
-13 + -12x + -1x2 = 0

Solving
-13 + -12x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(13 + 12x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(13 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
13 + 12x + x2 = 0

Solving
13 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + 12x + -13 + x2 = 0 + -13

Reorder the terms:
13 + -13 + 12x + x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 12x + x2 = 0 + -13
12x + x2 = 0 + -13

Combine like terms: 0 + -13 = -13
12x + x2 = -13

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 = -13 + 36

Reorder the terms:
36 + 12x + x2 = -13 + 36

Combine like terms: -13 + 36 = 23
36 + 12x + x2 = 23

Factor a perfect square on the left side:
(x + 6)(x + 6) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(x + 6) equal to 4.795831523 and -4.795831523.

Subproblem 1
x + 6 = 4.795831523

Simplifying
x + 6 = 4.795831523

Reorder the terms:
6 + x = 4.795831523

Solving
6 + x = 4.795831523

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 = 4.795831523 + -6

Combine like terms: 6 + -6 = 0
0 + x = 4.795831523 + -6
x = 4.795831523 + -6

Combine like terms: 4.795831523 + -6 = -1.204168477
x = -1.204168477

Simplifying
x = -1.204168477

Subproblem 2
x + 6 = -4.795831523

Simplifying
x + 6 = -4.795831523

Reorder the terms:
6 + x = -4.795831523

Solving
6 + x = -4.795831523

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 = -4.795831523 + -6

Combine like terms: 6 + -6 = 0
0 + x = -4.795831523 + -6
x = -4.795831523 + -6

Combine like terms: -4.795831523 + -6 = -10.795831523
x = -10.795831523

Simplifying
x = -10.795831523

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.204168477, -10.795831523}
Solution
x = {-1.204168477, -10.795831523}