6x^2-16x-370=0

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Solution for 6x^2-16x-370=0 equation: 


Simplifying
6x2 + -16x + -370 = 0

Reorder the terms:
-370 + -16x + 6x2 = 0

Solving
-370 + -16x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-185 + -8x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-185 + -8x + 3x2)' equal to zero and attempt to solve:

Simplifying
-185 + -8x + 3x2 = 0

Solving
-185 + -8x + 3x2 = 0

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

Divide each side by '3'.
-61.66666667 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '61.66666667' to each side of the equation.
-61.66666667 + -2.666666667x + 61.66666667 + x2 = 0 + 61.66666667

Reorder the terms:
-61.66666667 + 61.66666667 + -2.666666667x + x2 = 0 + 61.66666667

Combine like terms: -61.66666667 + 61.66666667 = 0.00000000
0.00000000 + -2.666666667x + x2 = 0 + 61.66666667
-2.666666667x + x2 = 0 + 61.66666667

Combine like terms: 0 + 61.66666667 = 61.66666667
-2.666666667x + x2 = 61.66666667

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = 61.66666667 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 61.66666667 + 1.777777780

Combine like terms: 61.66666667 + 1.777777780 = 63.44444445
1.777777780 + -2.666666667x + x2 = 63.44444445

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 63.44444445

Calculate the square root of the right side: 7.965202097

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 7.965202097 and -7.965202097.


Subproblem 1
x + -1.333333334 = 7.965202097

Simplifying
x + -1.333333334 = 7.965202097

Reorder the terms:
-1.333333334 + x = 7.965202097

Solving
-1.333333334 + x = 7.965202097

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 7.965202097 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 7.965202097 + 1.333333334
x = 7.965202097 + 1.333333334

Combine like terms: 7.965202097 + 1.333333334 = 9.298535431
x = 9.298535431

Simplifying
x = 9.298535431


Subproblem 2
x + -1.333333334 = -7.965202097

Simplifying
x + -1.333333334 = -7.965202097

Reorder the terms:
-1.333333334 + x = -7.965202097

Solving
-1.333333334 + x = -7.965202097

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -7.965202097 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -7.965202097 + 1.333333334
x = -7.965202097 + 1.333333334

Combine like terms: -7.965202097 + 1.333333334 = -6.631868763
x = -6.631868763

Simplifying
x = -6.631868763


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.298535431, -6.631868763}
Solution
x = {9.298535431, -6.631868763}

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