6x^2-12x-50=0

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Solution for 6x^2-12x-50=0 equation: 


Simplifying
6x2 + -12x + -50 = 0

Reorder the terms:
-50 + -12x + 6x2 = 0

Solving
-50 + -12x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + -6x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-25 + -6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-25 + -6x + 3x2 = 0

Solving
-25 + -6x + 3x2 = 0

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

Divide each side by '3'.
-8.333333333 + -2x + x2 = 0

Move the constant term to the right:

Add '8.333333333' to each side of the equation.
-8.333333333 + -2x + 8.333333333 + x2 = 0 + 8.333333333

Reorder the terms:
-8.333333333 + 8.333333333 + -2x + x2 = 0 + 8.333333333

Combine like terms: -8.333333333 + 8.333333333 = 0.000000000
0.000000000 + -2x + x2 = 0 + 8.333333333
-2x + x2 = 0 + 8.333333333

Combine like terms: 0 + 8.333333333 = 8.333333333
-2x + x2 = 8.333333333

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 = 8.333333333 + 1

Reorder the terms:
1 + -2x + x2 = 8.333333333 + 1

Combine like terms: 8.333333333 + 1 = 9.333333333
1 + -2x + x2 = 9.333333333

Factor a perfect square on the left side:
(x + -1)(x + -1) = 9.333333333

Calculate the square root of the right side: 3.055050463

Break this problem into two subproblems by setting 
(x + -1) equal to 3.055050463 and -3.055050463.


Subproblem 1
x + -1 = 3.055050463

Simplifying
x + -1 = 3.055050463

Reorder the terms:
-1 + x = 3.055050463

Solving
-1 + x = 3.055050463

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 = 3.055050463 + 1

Combine like terms: -1 + 1 = 0
0 + x = 3.055050463 + 1
x = 3.055050463 + 1

Combine like terms: 3.055050463 + 1 = 4.055050463
x = 4.055050463

Simplifying
x = 4.055050463


Subproblem 2
x + -1 = -3.055050463

Simplifying
x + -1 = -3.055050463

Reorder the terms:
-1 + x = -3.055050463

Solving
-1 + x = -3.055050463

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 = -3.055050463 + 1

Combine like terms: -1 + 1 = 0
0 + x = -3.055050463 + 1
x = -3.055050463 + 1

Combine like terms: -3.055050463 + 1 = -2.055050463
x = -2.055050463

Simplifying
x = -2.055050463


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.055050463, -2.055050463}
Solution
x = {4.055050463, -2.055050463}

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