x^2-x-1800=0

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

Simplifying
x2 + -1x + -1800 = 0

Reorder the terms:
-1800 + -1x + x2 = 0

Solving
-1800 + -1x + 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 + -1x + 1800 + x2 = 0 + 1800

Reorder the terms:
-1800 + 1800 + -1x + x2 = 0 + 1800

Combine like terms: -1800 + 1800 = 0
0 + -1x + x2 = 0 + 1800
-1x + x2 = 0 + 1800

Combine like terms: 0 + 1800 = 1800
-1x + x2 = 1800

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 1800 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 1800 + 0.25

Combine like terms: 1800 + 0.25 = 1800.25
0.25 + -1x + x2 = 1800.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1800.25

Calculate the square root of the right side: 42.429353047

Break this problem into two subproblems by setting 
(x + -0.5) equal to 42.429353047 and -42.429353047.

Subproblem 1
x + -0.5 = 42.429353047

Simplifying
x + -0.5 = 42.429353047

Reorder the terms:
-0.5 + x = 42.429353047

Solving
-0.5 + x = 42.429353047

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 42.429353047 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 42.429353047 + 0.5
x = 42.429353047 + 0.5

Combine like terms: 42.429353047 + 0.5 = 42.929353047
x = 42.929353047

Simplifying
x = 42.929353047

Subproblem 2
x + -0.5 = -42.429353047

Simplifying
x + -0.5 = -42.429353047

Reorder the terms:
-0.5 + x = -42.429353047

Solving
-0.5 + x = -42.429353047

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -42.429353047 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -42.429353047 + 0.5
x = -42.429353047 + 0.5

Combine like terms: -42.429353047 + 0.5 = -41.929353047
x = -41.929353047

Simplifying
x = -41.929353047

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {42.929353047, -41.929353047}