6x^2-18000x-1800000=0

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Solution for 6x^2-18000x-1800000=0 equation: 


Simplifying
6x2 + -18000x + -1800000 = 0

Reorder the terms:
-1800000 + -18000x + 6x2 = 0

Solving
-1800000 + -18000x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-300000 + -3000x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-300000 + -3000x + x2)' equal to zero and attempt to solve:

Simplifying
-300000 + -3000x + x2 = 0

Solving
-300000 + -3000x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '300000' to each side of the equation.
-300000 + -3000x + 300000 + x2 = 0 + 300000

Reorder the terms:
-300000 + 300000 + -3000x + x2 = 0 + 300000

Combine like terms: -300000 + 300000 = 0
0 + -3000x + x2 = 0 + 300000
-3000x + x2 = 0 + 300000

Combine like terms: 0 + 300000 = 300000
-3000x + x2 = 300000

The x term is -3000x.  Take half its coefficient (-1500).
Square it (2250000) and add it to both sides.

Add '2250000' to each side of the equation.
-3000x + 2250000 + x2 = 300000 + 2250000

Reorder the terms:
2250000 + -3000x + x2 = 300000 + 2250000

Combine like terms: 300000 + 2250000 = 2550000
2250000 + -3000x + x2 = 2550000

Factor a perfect square on the left side:
(x + -1500)(x + -1500) = 2550000

Calculate the square root of the right side: 1596.871942267

Break this problem into two subproblems by setting 
(x + -1500) equal to 1596.871942267 and -1596.871942267.


Subproblem 1
x + -1500 = 1596.871942267

Simplifying
x + -1500 = 1596.871942267

Reorder the terms:
-1500 + x = 1596.871942267

Solving
-1500 + x = 1596.871942267

Solving for variable 'x'.

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

Add '1500' to each side of the equation.
-1500 + 1500 + x = 1596.871942267 + 1500

Combine like terms: -1500 + 1500 = 0
0 + x = 1596.871942267 + 1500
x = 1596.871942267 + 1500

Combine like terms: 1596.871942267 + 1500 = 3096.871942267
x = 3096.871942267

Simplifying
x = 3096.871942267


Subproblem 2
x + -1500 = -1596.871942267

Simplifying
x + -1500 = -1596.871942267

Reorder the terms:
-1500 + x = -1596.871942267

Solving
-1500 + x = -1596.871942267

Solving for variable 'x'.

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

Add '1500' to each side of the equation.
-1500 + 1500 + x = -1596.871942267 + 1500

Combine like terms: -1500 + 1500 = 0
0 + x = -1596.871942267 + 1500
x = -1596.871942267 + 1500

Combine like terms: -1596.871942267 + 1500 = -96.871942267
x = -96.871942267

Simplifying
x = -96.871942267


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3096.871942267, -96.871942267}
Solution
x = {3096.871942267, -96.871942267}

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