-6x^2+300x-1000=0

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Solution for -6x^2+300x-1000=0 equation: 


Simplifying
-6x2 + 300x + -1000 = 0

Reorder the terms:
-1000 + 300x + -6x2 = 0

Solving
-1000 + 300x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-500 + 150x + -3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-500 + 150x + -3x2)' equal to zero and attempt to solve:

Simplifying
-500 + 150x + -3x2 = 0

Solving
-500 + 150x + -3x2 = 0

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

Divide each side by '-3'.
166.6666667 + -50x + x2 = 0

Move the constant term to the right:

Add '-166.6666667' to each side of the equation.
166.6666667 + -50x + -166.6666667 + x2 = 0 + -166.6666667

Reorder the terms:
166.6666667 + -166.6666667 + -50x + x2 = 0 + -166.6666667

Combine like terms: 166.6666667 + -166.6666667 = 0.0000000
0.0000000 + -50x + x2 = 0 + -166.6666667
-50x + x2 = 0 + -166.6666667

Combine like terms: 0 + -166.6666667 = -166.6666667
-50x + x2 = -166.6666667

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 = -166.6666667 + 625

Reorder the terms:
625 + -50x + x2 = -166.6666667 + 625

Combine like terms: -166.6666667 + 625 = 458.3333333
625 + -50x + x2 = 458.3333333

Factor a perfect square on the left side:
(x + -25)(x + -25) = 458.3333333

Calculate the square root of the right side: 21.408720964

Break this problem into two subproblems by setting 
(x + -25) equal to 21.408720964 and -21.408720964.


Subproblem 1
x + -25 = 21.408720964

Simplifying
x + -25 = 21.408720964

Reorder the terms:
-25 + x = 21.408720964

Solving
-25 + x = 21.408720964

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 = 21.408720964 + 25

Combine like terms: -25 + 25 = 0
0 + x = 21.408720964 + 25
x = 21.408720964 + 25

Combine like terms: 21.408720964 + 25 = 46.408720964
x = 46.408720964

Simplifying
x = 46.408720964


Subproblem 2
x + -25 = -21.408720964

Simplifying
x + -25 = -21.408720964

Reorder the terms:
-25 + x = -21.408720964

Solving
-25 + x = -21.408720964

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 = -21.408720964 + 25

Combine like terms: -25 + 25 = 0
0 + x = -21.408720964 + 25
x = -21.408720964 + 25

Combine like terms: -21.408720964 + 25 = 3.591279036
x = 3.591279036

Simplifying
x = 3.591279036


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {46.408720964, 3.591279036}
Solution
x = {46.408720964, 3.591279036}

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