-6x^2+300x-3000=0

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Solution for -6x^2+300x-3000=0 equation: 


Simplifying
-6x2 + 300x + -3000 = 0

Reorder the terms:
-3000 + 300x + -6x2 = 0

Solving
-3000 + 300x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-500 + 50x + -1x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-500 + 50x + -1x2)' equal to zero and attempt to solve:

Simplifying
-500 + 50x + -1x2 = 0

Solving
-500 + 50x + -1x2 = 0

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

Divide each side by '-1'.
500 + -50x + x2 = 0

Move the constant term to the right:

Add '-500' to each side of the equation.
500 + -50x + -500 + x2 = 0 + -500

Reorder the terms:
500 + -500 + -50x + x2 = 0 + -500

Combine like terms: 500 + -500 = 0
0 + -50x + x2 = 0 + -500
-50x + x2 = 0 + -500

Combine like terms: 0 + -500 = -500
-50x + x2 = -500

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 = -500 + 625

Reorder the terms:
625 + -50x + x2 = -500 + 625

Combine like terms: -500 + 625 = 125
625 + -50x + x2 = 125

Factor a perfect square on the left side:
(x + -25)(x + -25) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(x + -25) equal to 11.180339887 and -11.180339887.


Subproblem 1
x + -25 = 11.180339887

Simplifying
x + -25 = 11.180339887

Reorder the terms:
-25 + x = 11.180339887

Solving
-25 + x = 11.180339887

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 = 11.180339887 + 25

Combine like terms: -25 + 25 = 0
0 + x = 11.180339887 + 25
x = 11.180339887 + 25

Combine like terms: 11.180339887 + 25 = 36.180339887
x = 36.180339887

Simplifying
x = 36.180339887


Subproblem 2
x + -25 = -11.180339887

Simplifying
x + -25 = -11.180339887

Reorder the terms:
-25 + x = -11.180339887

Solving
-25 + x = -11.180339887

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 = -11.180339887 + 25

Combine like terms: -25 + 25 = 0
0 + x = -11.180339887 + 25
x = -11.180339887 + 25

Combine like terms: -11.180339887 + 25 = 13.819660113
x = 13.819660113

Simplifying
x = 13.819660113


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {36.180339887, 13.819660113}
Solution
x = {36.180339887, 13.819660113}

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