x^2+13x-58=0

Solution for x^2+13x-58=0 equation:

Simplifying
x2 + 13x + -58 = 0

Reorder the terms:
-58 + 13x + x2 = 0

Solving
-58 + 13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '58' to each side of the equation.
-58 + 13x + 58 + x2 = 0 + 58

Reorder the terms:
-58 + 58 + 13x + x2 = 0 + 58

Combine like terms: -58 + 58 = 0
0 + 13x + x2 = 0 + 58
13x + x2 = 0 + 58

Combine like terms: 0 + 58 = 58
13x + x2 = 58

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 = 58 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 58 + 42.25

Combine like terms: 58 + 42.25 = 100.25
42.25 + 13x + x2 = 100.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(x + 6.5) equal to 10.012492197 and -10.012492197.

Subproblem 1
x + 6.5 = 10.012492197

Simplifying
x + 6.5 = 10.012492197

Reorder the terms:
6.5 + x = 10.012492197

Solving
6.5 + x = 10.012492197

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 = 10.012492197 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 10.012492197 + -6.5
x = 10.012492197 + -6.5

Combine like terms: 10.012492197 + -6.5 = 3.512492197
x = 3.512492197

Simplifying
x = 3.512492197

Subproblem 2
x + 6.5 = -10.012492197

Simplifying
x + 6.5 = -10.012492197

Reorder the terms:
6.5 + x = -10.012492197

Solving
6.5 + x = -10.012492197

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 = -10.012492197 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -10.012492197 + -6.5
x = -10.012492197 + -6.5

Combine like terms: -10.012492197 + -6.5 = -16.512492197
x = -16.512492197

Simplifying
x = -16.512492197

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.512492197, -16.512492197}