x^2+6x-1800=0

Solution for x^2+6x-1800=0 equation:

Simplifying
x2 + 6x + -1800 = 0

Reorder the terms:
-1800 + 6x + x2 = 0

Solving
-1800 + 6x + 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 + 6x + 1800 + x2 = 0 + 1800

Reorder the terms:
-1800 + 1800 + 6x + x2 = 0 + 1800

Combine like terms: -1800 + 1800 = 0
0 + 6x + x2 = 0 + 1800
6x + x2 = 0 + 1800

Combine like terms: 0 + 1800 = 1800
6x + x2 = 1800

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 1800 + 9

Reorder the terms:
9 + 6x + x2 = 1800 + 9

Combine like terms: 1800 + 9 = 1809
9 + 6x + x2 = 1809

Factor a perfect square on the left side:
(x + 3)(x + 3) = 1809

Calculate the square root of the right side: 42.532340636

Break this problem into two subproblems by setting 
(x + 3) equal to 42.532340636 and -42.532340636.

Subproblem 1
x + 3 = 42.532340636

Simplifying
x + 3 = 42.532340636

Reorder the terms:
3 + x = 42.532340636

Solving
3 + x = 42.532340636

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 42.532340636 + -3

Combine like terms: 3 + -3 = 0
0 + x = 42.532340636 + -3
x = 42.532340636 + -3

Combine like terms: 42.532340636 + -3 = 39.532340636
x = 39.532340636

Simplifying
x = 39.532340636

Subproblem 2
x + 3 = -42.532340636

Simplifying
x + 3 = -42.532340636

Reorder the terms:
3 + x = -42.532340636

Solving
3 + x = -42.532340636

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -42.532340636 + -3

Combine like terms: 3 + -3 = 0
0 + x = -42.532340636 + -3
x = -42.532340636 + -3

Combine like terms: -42.532340636 + -3 = -45.532340636
x = -45.532340636

Simplifying
x = -45.532340636

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {39.532340636, -45.532340636}