x^2+15x=10029

Solution for x^2+15x=10029 equation:

Simplifying
x2 + 15x = 10029

Reorder the terms:
15x + x2 = 10029

Solving
15x + x2 = 10029

Solving for variable 'x'.

Reorder the terms:
-10029 + 15x + x2 = 10029 + -10029

Combine like terms: 10029 + -10029 = 0
-10029 + 15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10029' to each side of the equation.
-10029 + 15x + 10029 + x2 = 0 + 10029

Reorder the terms:
-10029 + 10029 + 15x + x2 = 0 + 10029

Combine like terms: -10029 + 10029 = 0
0 + 15x + x2 = 0 + 10029
15x + x2 = 0 + 10029

Combine like terms: 0 + 10029 = 10029
15x + x2 = 10029

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = 10029 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 10029 + 56.25

Combine like terms: 10029 + 56.25 = 10085.25
56.25 + 15x + x2 = 10085.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 10085.25

Calculate the square root of the right side: 100.425345406

Break this problem into two subproblems by setting 
(x + 7.5) equal to 100.425345406 and -100.425345406.

Subproblem 1
x + 7.5 = 100.425345406

Simplifying
x + 7.5 = 100.425345406

Reorder the terms:
7.5 + x = 100.425345406

Solving
7.5 + x = 100.425345406

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 100.425345406 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 100.425345406 + -7.5
x = 100.425345406 + -7.5

Combine like terms: 100.425345406 + -7.5 = 92.925345406
x = 92.925345406

Simplifying
x = 92.925345406

Subproblem 2
x + 7.5 = -100.425345406

Simplifying
x + 7.5 = -100.425345406

Reorder the terms:
7.5 + x = -100.425345406

Solving
7.5 + x = -100.425345406

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -100.425345406 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -100.425345406 + -7.5
x = -100.425345406 + -7.5

Combine like terms: -100.425345406 + -7.5 = -107.925345406
x = -107.925345406

Simplifying
x = -107.925345406

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {92.925345406, -107.925345406}