-x^2-23x-6=0

Solution for -x^2-23x-6=0 equation:

Simplifying
-1x2 + -23x + -6 = 0

Reorder the terms:
-6 + -23x + -1x2 = 0

Solving
-6 + -23x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 23x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 23x + x2)' equal to zero and attempt to solve:

Simplifying
6 + 23x + x2 = 0

Solving
6 + 23x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 23x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 23x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 23x + x2 = 0 + -6
23x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
23x + x2 = -6

The x term is 23x.  Take half its coefficient (11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
23x + 132.25 + x2 = -6 + 132.25

Reorder the terms:
132.25 + 23x + x2 = -6 + 132.25

Combine like terms: -6 + 132.25 = 126.25
132.25 + 23x + x2 = 126.25

Factor a perfect square on the left side:
(x + 11.5)(x + 11.5) = 126.25

Calculate the square root of the right side: 11.236102527

Break this problem into two subproblems by setting 
(x + 11.5) equal to 11.236102527 and -11.236102527.

Subproblem 1
x + 11.5 = 11.236102527

Simplifying
x + 11.5 = 11.236102527

Reorder the terms:
11.5 + x = 11.236102527

Solving
11.5 + x = 11.236102527

Solving for variable 'x'.

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

Add '-11.5' to each side of the equation.
11.5 + -11.5 + x = 11.236102527 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + x = 11.236102527 + -11.5
x = 11.236102527 + -11.5

Combine like terms: 11.236102527 + -11.5 = -0.263897473
x = -0.263897473

Simplifying
x = -0.263897473

Subproblem 2
x + 11.5 = -11.236102527

Simplifying
x + 11.5 = -11.236102527

Reorder the terms:
11.5 + x = -11.236102527

Solving
11.5 + x = -11.236102527

Solving for variable 'x'.

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

Add '-11.5' to each side of the equation.
11.5 + -11.5 + x = -11.236102527 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + x = -11.236102527 + -11.5
x = -11.236102527 + -11.5

Combine like terms: -11.236102527 + -11.5 = -22.736102527
x = -22.736102527

Simplifying
x = -22.736102527

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.263897473, -22.736102527}
Solution
x = {-0.263897473, -22.736102527}