-6x^2+300x-2000=0

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Solution for -6x^2+300x-2000=0 equation: 


Simplifying
-6x2 + 300x + -2000 = 0

Reorder the terms:
-2000 + 300x + -6x2 = 0

Solving
-2000 + 300x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1000 + 150x + -3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1000 + 150x + -3x2)' equal to zero and attempt to solve:

Simplifying
-1000 + 150x + -3x2 = 0

Solving
-1000 + 150x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
333.3333333 + -50x + x2 = 0

Move the constant term to the right:

Add '-333.3333333' to each side of the equation.
333.3333333 + -50x + -333.3333333 + x2 = 0 + -333.3333333

Reorder the terms:
333.3333333 + -333.3333333 + -50x + x2 = 0 + -333.3333333

Combine like terms: 333.3333333 + -333.3333333 = 0.0000000
0.0000000 + -50x + x2 = 0 + -333.3333333
-50x + x2 = 0 + -333.3333333

Combine like terms: 0 + -333.3333333 = -333.3333333
-50x + x2 = -333.3333333

The x term is -50x.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50x + 625 + x2 = -333.3333333 + 625

Reorder the terms:
625 + -50x + x2 = -333.3333333 + 625

Combine like terms: -333.3333333 + 625 = 291.6666667
625 + -50x + x2 = 291.6666667

Factor a perfect square on the left side:
(x + -25)(x + -25) = 291.6666667

Calculate the square root of the right side: 17.078251278

Break this problem into two subproblems by setting 
(x + -25) equal to 17.078251278 and -17.078251278.


Subproblem 1
x + -25 = 17.078251278

Simplifying
x + -25 = 17.078251278

Reorder the terms:
-25 + x = 17.078251278

Solving
-25 + x = 17.078251278

Solving for variable 'x'.

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

Add '25' to each side of the equation.
-25 + 25 + x = 17.078251278 + 25

Combine like terms: -25 + 25 = 0
0 + x = 17.078251278 + 25
x = 17.078251278 + 25

Combine like terms: 17.078251278 + 25 = 42.078251278
x = 42.078251278

Simplifying
x = 42.078251278


Subproblem 2
x + -25 = -17.078251278

Simplifying
x + -25 = -17.078251278

Reorder the terms:
-25 + x = -17.078251278

Solving
-25 + x = -17.078251278

Solving for variable 'x'.

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

Add '25' to each side of the equation.
-25 + 25 + x = -17.078251278 + 25

Combine like terms: -25 + 25 = 0
0 + x = -17.078251278 + 25
x = -17.078251278 + 25

Combine like terms: -17.078251278 + 25 = 7.921748722
x = 7.921748722

Simplifying
x = 7.921748722


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {42.078251278, 7.921748722}
Solution
x = {42.078251278, 7.921748722}

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