6x^2-12x-1300=0

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Solution for 6x^2-12x-1300=0 equation: 


Simplifying
6x2 + -12x + -1300 = 0

Reorder the terms:
-1300 + -12x + 6x2 = 0

Solving
-1300 + -12x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-650 + -6x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-650 + -6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-650 + -6x + 3x2 = 0

Solving
-650 + -6x + 3x2 = 0

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

Divide each side by '3'.
-216.6666667 + -2x + x2 = 0

Move the constant term to the right:

Add '216.6666667' to each side of the equation.
-216.6666667 + -2x + 216.6666667 + x2 = 0 + 216.6666667

Reorder the terms:
-216.6666667 + 216.6666667 + -2x + x2 = 0 + 216.6666667

Combine like terms: -216.6666667 + 216.6666667 = 0.0000000
0.0000000 + -2x + x2 = 0 + 216.6666667
-2x + x2 = 0 + 216.6666667

Combine like terms: 0 + 216.6666667 = 216.6666667
-2x + x2 = 216.6666667

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 216.6666667 + 1

Reorder the terms:
1 + -2x + x2 = 216.6666667 + 1

Combine like terms: 216.6666667 + 1 = 217.6666667
1 + -2x + x2 = 217.6666667

Factor a perfect square on the left side:
(x + -1)(x + -1) = 217.6666667

Calculate the square root of the right side: 14.753530652

Break this problem into two subproblems by setting 
(x + -1) equal to 14.753530652 and -14.753530652.


Subproblem 1
x + -1 = 14.753530652

Simplifying
x + -1 = 14.753530652

Reorder the terms:
-1 + x = 14.753530652

Solving
-1 + x = 14.753530652

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 14.753530652 + 1

Combine like terms: -1 + 1 = 0
0 + x = 14.753530652 + 1
x = 14.753530652 + 1

Combine like terms: 14.753530652 + 1 = 15.753530652
x = 15.753530652

Simplifying
x = 15.753530652


Subproblem 2
x + -1 = -14.753530652

Simplifying
x + -1 = -14.753530652

Reorder the terms:
-1 + x = -14.753530652

Solving
-1 + x = -14.753530652

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -14.753530652 + 1

Combine like terms: -1 + 1 = 0
0 + x = -14.753530652 + 1
x = -14.753530652 + 1

Combine like terms: -14.753530652 + 1 = -13.753530652
x = -13.753530652

Simplifying
x = -13.753530652


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.753530652, -13.753530652}
Solution
x = {15.753530652, -13.753530652}

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