x^2+13x-20=0

Solution for x^2+13x-20=0 equation:

Simplifying
x2 + 13x + -20 = 0

Reorder the terms:
-20 + 13x + x2 = 0

Solving
-20 + 13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 13x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 13x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 13x + x2 = 0 + 20
13x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
13x + x2 = 20

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 = 20 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 20 + 42.25

Combine like terms: 20 + 42.25 = 62.25
42.25 + 13x + x2 = 62.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(x + 6.5) equal to 7.889866919 and -7.889866919.

Subproblem 1
x + 6.5 = 7.889866919

Simplifying
x + 6.5 = 7.889866919

Reorder the terms:
6.5 + x = 7.889866919

Solving
6.5 + x = 7.889866919

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 = 7.889866919 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 7.889866919 + -6.5
x = 7.889866919 + -6.5

Combine like terms: 7.889866919 + -6.5 = 1.389866919
x = 1.389866919

Simplifying
x = 1.389866919

Subproblem 2
x + 6.5 = -7.889866919

Simplifying
x + 6.5 = -7.889866919

Reorder the terms:
6.5 + x = -7.889866919

Solving
6.5 + x = -7.889866919

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 = -7.889866919 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -7.889866919 + -6.5
x = -7.889866919 + -6.5

Combine like terms: -7.889866919 + -6.5 = -14.389866919
x = -14.389866919

Simplifying
x = -14.389866919

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.389866919, -14.389866919}