x^2-6x-1800=0

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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 = 45.532340636 x = 45.532340636 Simplifying x = 45.532340636

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 = -39.532340636 x = -39.532340636 Simplifying x = -39.532340636

Solution

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

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