13x+x^2=10044

Solution for 13x+x^2=10044 equation:

Simplifying
13x + x2 = 10044

Solving
13x + x2 = 10044

Solving for variable 'x'.

Reorder the terms:
-10044 + 13x + x2 = 10044 + -10044

Combine like terms: 10044 + -10044 = 0
-10044 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10044' to each side of the equation.
-10044 + 13x + 10044 + x2 = 0 + 10044

Reorder the terms:
-10044 + 10044 + 13x + x2 = 0 + 10044

Combine like terms: -10044 + 10044 = 0
0 + 13x + x2 = 0 + 10044
13x + x2 = 0 + 10044

Combine like terms: 0 + 10044 = 10044
13x + x2 = 10044

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 = 10044 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 10044 + 42.25

Combine like terms: 10044 + 42.25 = 10086.25
42.25 + 13x + x2 = 10086.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 10086.25

Calculate the square root of the right side: 100.430324106

Break this problem into two subproblems by setting 
(x + 6.5) equal to 100.430324106 and -100.430324106.

Subproblem 1
x + 6.5 = 100.430324106

Simplifying
x + 6.5 = 100.430324106

Reorder the terms:
6.5 + x = 100.430324106

Solving
6.5 + x = 100.430324106

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 = 100.430324106 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 100.430324106 + -6.5
x = 100.430324106 + -6.5

Combine like terms: 100.430324106 + -6.5 = 93.930324106
x = 93.930324106

Simplifying
x = 93.930324106

Subproblem 2
x + 6.5 = -100.430324106

Simplifying
x + 6.5 = -100.430324106

Reorder the terms:
6.5 + x = -100.430324106

Solving
6.5 + x = -100.430324106

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 = -100.430324106 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -100.430324106 + -6.5
x = -100.430324106 + -6.5

Combine like terms: -100.430324106 + -6.5 = -106.930324106
x = -106.930324106

Simplifying
x = -106.930324106

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {93.930324106, -106.930324106}