x^2-13x-130=0

Solution for x^2-13x-130=0 equation:

Simplifying
x2 + -13x + -130 = 0

Reorder the terms:
-130 + -13x + x2 = 0

Solving
-130 + -13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '130' to each side of the equation.
-130 + -13x + 130 + x2 = 0 + 130

Reorder the terms:
-130 + 130 + -13x + x2 = 0 + 130

Combine like terms: -130 + 130 = 0
0 + -13x + x2 = 0 + 130
-13x + x2 = 0 + 130

Combine like terms: 0 + 130 = 130
-13x + x2 = 130

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 = 130 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 130 + 42.25

Combine like terms: 130 + 42.25 = 172.25
42.25 + -13x + x2 = 172.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 172.25

Calculate the square root of the right side: 13.124404748

Break this problem into two subproblems by setting 
(x + -6.5) equal to 13.124404748 and -13.124404748.

Subproblem 1
x + -6.5 = 13.124404748

Simplifying
x + -6.5 = 13.124404748

Reorder the terms:
-6.5 + x = 13.124404748

Solving
-6.5 + x = 13.124404748

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 = 13.124404748 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 13.124404748 + 6.5
x = 13.124404748 + 6.5

Combine like terms: 13.124404748 + 6.5 = 19.624404748
x = 19.624404748

Simplifying
x = 19.624404748

Subproblem 2
x + -6.5 = -13.124404748

Simplifying
x + -6.5 = -13.124404748

Reorder the terms:
-6.5 + x = -13.124404748

Solving
-6.5 + x = -13.124404748

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 = -13.124404748 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -13.124404748 + 6.5
x = -13.124404748 + 6.5

Combine like terms: -13.124404748 + 6.5 = -6.624404748
x = -6.624404748

Simplifying
x = -6.624404748

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.624404748, -6.624404748}