-x^2-13x-2=0

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


Simplifying
-1x2 + -13x + -2 = 0

Reorder the terms:
-2 + -13x + -1x2 = 0

Solving
-2 + -13x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 13x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(2 + 13x + x2)' equal to zero and attempt to solve:

Simplifying
2 + 13x + x2 = 0

Solving
2 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 13x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 13x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 13x + x2 = 0 + -2
13x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
13x + x2 = -2

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = -2 + 42.25

Reorder the terms:
42.25 + 13x + x2 = -2 + 42.25

Combine like terms: -2 + 42.25 = 40.25
42.25 + 13x + x2 = 40.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(x + 6.5) equal to 6.34428877 and -6.34428877.


Subproblem 1
x + 6.5 = 6.34428877

Simplifying
x + 6.5 = 6.34428877

Reorder the terms:
6.5 + x = 6.34428877

Solving
6.5 + x = 6.34428877

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 6.34428877 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 6.34428877 + -6.5
x = 6.34428877 + -6.5

Combine like terms: 6.34428877 + -6.5 = -0.15571123
x = -0.15571123

Simplifying
x = -0.15571123


Subproblem 2
x + 6.5 = -6.34428877

Simplifying
x + 6.5 = -6.34428877

Reorder the terms:
6.5 + x = -6.34428877

Solving
6.5 + x = -6.34428877

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -6.34428877 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -6.34428877 + -6.5
x = -6.34428877 + -6.5

Combine like terms: -6.34428877 + -6.5 = -12.84428877
x = -12.84428877

Simplifying
x = -12.84428877


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.15571123, -12.84428877}
Solution
x = {-0.15571123, -12.84428877}

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