x^2-13x-5=0

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Solution for x^2-13x-5=0 equation: 


Simplifying
x2 + -13x + -5 = 0

Reorder the terms:
-5 + -13x + x2 = 0

Solving
-5 + -13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -13x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -13x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -13x + x2 = 0 + 5
-13x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-13x + x2 = 5

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 = 5 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 5 + 42.25

Combine like terms: 5 + 42.25 = 47.25
42.25 + -13x + x2 = 47.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 47.25

Calculate the square root of the right side: 6.873863542

Break this problem into two subproblems by setting 
(x + -6.5) equal to 6.873863542 and -6.873863542.


Subproblem 1
x + -6.5 = 6.873863542

Simplifying
x + -6.5 = 6.873863542

Reorder the terms:
-6.5 + x = 6.873863542

Solving
-6.5 + x = 6.873863542

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 = 6.873863542 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 6.873863542 + 6.5
x = 6.873863542 + 6.5

Combine like terms: 6.873863542 + 6.5 = 13.373863542
x = 13.373863542

Simplifying
x = 13.373863542


Subproblem 2
x + -6.5 = -6.873863542

Simplifying
x + -6.5 = -6.873863542

Reorder the terms:
-6.5 + x = -6.873863542

Solving
-6.5 + x = -6.873863542

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 = -6.873863542 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -6.873863542 + 6.5
x = -6.873863542 + 6.5

Combine like terms: -6.873863542 + 6.5 = -0.373863542
x = -0.373863542

Simplifying
x = -0.373863542


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.373863542, -0.373863542}

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