x^2-15x-1800=0

Solution for x^2-15x-1800=0 equation:

Simplifying
x2 + -15x + -1800 = 0

Reorder the terms:
-1800 + -15x + x2 = 0

Solving
-1800 + -15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1800' to each side of the equation.
-1800 + -15x + 1800 + x2 = 0 + 1800

Reorder the terms:
-1800 + 1800 + -15x + x2 = 0 + 1800

Combine like terms: -1800 + 1800 = 0
0 + -15x + x2 = 0 + 1800
-15x + x2 = 0 + 1800

Combine like terms: 0 + 1800 = 1800
-15x + x2 = 1800

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 = 1800 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 1800 + 56.25

Combine like terms: 1800 + 56.25 = 1856.25
56.25 + -15x + x2 = 1856.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 1856.25

Calculate the square root of the right side: 43.084219849

Break this problem into two subproblems by setting 
(x + -7.5) equal to 43.084219849 and -43.084219849.

Subproblem 1
x + -7.5 = 43.084219849

Simplifying
x + -7.5 = 43.084219849

Reorder the terms:
-7.5 + x = 43.084219849

Solving
-7.5 + x = 43.084219849

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 = 43.084219849 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 43.084219849 + 7.5
x = 43.084219849 + 7.5

Combine like terms: 43.084219849 + 7.5 = 50.584219849
x = 50.584219849

Simplifying
x = 50.584219849

Subproblem 2
x + -7.5 = -43.084219849

Simplifying
x + -7.5 = -43.084219849

Reorder the terms:
-7.5 + x = -43.084219849

Solving
-7.5 + x = -43.084219849

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 = -43.084219849 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -43.084219849 + 7.5
x = -43.084219849 + 7.5

Combine like terms: -43.084219849 + 7.5 = -35.584219849
x = -35.584219849

Simplifying
x = -35.584219849

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {50.584219849, -35.584219849}