-6x^2+12000x-1800000=0

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Solution for -6x^2+12000x-1800000=0 equation: 


Simplifying
-6x2 + 12000x + -1800000 = 0

Reorder the terms:
-1800000 + 12000x + -6x2 = 0

Solving
-1800000 + 12000x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-300000 + 2000x + -1x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-300000 + 2000x + -1x2)' equal to zero and attempt to solve:

Simplifying
-300000 + 2000x + -1x2 = 0

Solving
-300000 + 2000x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
300000 + -2000x + x2 = 0

Move the constant term to the right:

Add '-300000' to each side of the equation.
300000 + -2000x + -300000 + x2 = 0 + -300000

Reorder the terms:
300000 + -300000 + -2000x + x2 = 0 + -300000

Combine like terms: 300000 + -300000 = 0
0 + -2000x + x2 = 0 + -300000
-2000x + x2 = 0 + -300000

Combine like terms: 0 + -300000 = -300000
-2000x + x2 = -300000

The x term is -2000x.  Take half its coefficient (-1000).
Square it (1000000) and add it to both sides.

Add '1000000' to each side of the equation.
-2000x + 1000000 + x2 = -300000 + 1000000

Reorder the terms:
1000000 + -2000x + x2 = -300000 + 1000000

Combine like terms: -300000 + 1000000 = 700000
1000000 + -2000x + x2 = 700000

Factor a perfect square on the left side:
(x + -1000)(x + -1000) = 700000

Calculate the square root of the right side: 836.660026534

Break this problem into two subproblems by setting 
(x + -1000) equal to 836.660026534 and -836.660026534.


Subproblem 1
x + -1000 = 836.660026534

Simplifying
x + -1000 = 836.660026534

Reorder the terms:
-1000 + x = 836.660026534

Solving
-1000 + x = 836.660026534

Solving for variable 'x'.

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

Add '1000' to each side of the equation.
-1000 + 1000 + x = 836.660026534 + 1000

Combine like terms: -1000 + 1000 = 0
0 + x = 836.660026534 + 1000
x = 836.660026534 + 1000

Combine like terms: 836.660026534 + 1000 = 1836.660026534
x = 1836.660026534

Simplifying
x = 1836.660026534


Subproblem 2
x + -1000 = -836.660026534

Simplifying
x + -1000 = -836.660026534

Reorder the terms:
-1000 + x = -836.660026534

Solving
-1000 + x = -836.660026534

Solving for variable 'x'.

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

Add '1000' to each side of the equation.
-1000 + 1000 + x = -836.660026534 + 1000

Combine like terms: -1000 + 1000 = 0
0 + x = -836.660026534 + 1000
x = -836.660026534 + 1000

Combine like terms: -836.660026534 + 1000 = 163.339973466
x = 163.339973466

Simplifying
x = 163.339973466


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1836.660026534, 163.339973466}
Solution
x = {1836.660026534, 163.339973466}

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