0=13x+x^2-60

Solution for 0=13x+x^2-60 equation:

Simplifying
0 = 13x + x2 + -60

Reorder the terms:
0 = -60 + 13x + x2

Solving
0 = -60 + 13x + x2

Solving for variable 'x'.

Combine like terms: 0 + 60 = 60
60 + -13x + -1x2 = -60 + 13x + x2 + 60 + -13x + -1x2

Reorder the terms:
60 + -13x + -1x2 = -60 + 60 + 13x + -13x + x2 + -1x2

Combine like terms: -60 + 60 = 0
60 + -13x + -1x2 = 0 + 13x + -13x + x2 + -1x2
60 + -13x + -1x2 = 13x + -13x + x2 + -1x2

Combine like terms: 13x + -13x = 0
60 + -13x + -1x2 = 0 + x2 + -1x2
60 + -13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
60 + -13x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-60 + 13x + x2 = 0

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 13x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 13x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 13x + x2 = 0 + 60
13x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
13x + x2 = 60

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 = 60 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 60 + 42.25

Combine like terms: 60 + 42.25 = 102.25
42.25 + 13x + x2 = 102.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 102.25

Calculate the square root of the right side: 10.111874208

Break this problem into two subproblems by setting 
(x + 6.5) equal to 10.111874208 and -10.111874208.

Subproblem 1
x + 6.5 = 10.111874208

Simplifying
x + 6.5 = 10.111874208

Reorder the terms:
6.5 + x = 10.111874208

Solving
6.5 + x = 10.111874208

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 = 10.111874208 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 10.111874208 + -6.5
x = 10.111874208 + -6.5

Combine like terms: 10.111874208 + -6.5 = 3.611874208
x = 3.611874208

Simplifying
x = 3.611874208

Subproblem 2
x + 6.5 = -10.111874208

Simplifying
x + 6.5 = -10.111874208

Reorder the terms:
6.5 + x = -10.111874208

Solving
6.5 + x = -10.111874208

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 = -10.111874208 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -10.111874208 + -6.5
x = -10.111874208 + -6.5

Combine like terms: -10.111874208 + -6.5 = -16.611874208
x = -16.611874208

Simplifying
x = -16.611874208

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.611874208, -16.611874208}