x^2-13x-1=0

Solution for x^2-13x-1=0 equation:

Simplifying
x2 + -13x + -1 = 0

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

Solving
-1 + -13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -13x + 1 + x2 = 0 + 1

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

Combine like terms: -1 + 1 = 0
0 + -13x + x2 = 0 + 1
-13x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-13x + x2 = 1

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 = 1 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 1 + 42.25

Combine like terms: 1 + 42.25 = 43.25
42.25 + -13x + x2 = 43.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 43.25

Calculate the square root of the right side: 6.576473219

Break this problem into two subproblems by setting 
(x + -6.5) equal to 6.576473219 and -6.576473219.

Subproblem 1
x + -6.5 = 6.576473219

Simplifying
x + -6.5 = 6.576473219

Reorder the terms:
-6.5 + x = 6.576473219

Solving
-6.5 + x = 6.576473219

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 = 6.576473219 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 6.576473219 + 6.5
x = 6.576473219 + 6.5

Combine like terms: 6.576473219 + 6.5 = 13.076473219
x = 13.076473219

Simplifying
x = 13.076473219

Subproblem 2
x + -6.5 = -6.576473219

Simplifying
x + -6.5 = -6.576473219

Reorder the terms:
-6.5 + x = -6.576473219

Solving
-6.5 + x = -6.576473219

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 = -6.576473219 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -6.576473219 + 6.5
x = -6.576473219 + 6.5

Combine like terms: -6.576473219 + 6.5 = -0.076473219
x = -0.076473219

Simplifying
x = -0.076473219

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.076473219, -0.076473219}