6x^2-39x-3=0

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Solution for 6x^2-39x-3=0 equation: 


Simplifying
6x2 + -39x + -3 = 0

Reorder the terms:
-3 + -39x + 6x2 = 0

Solving
-3 + -39x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -13x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1 + -13x + 2x2)' equal to zero and attempt to solve:

Simplifying
-1 + -13x + 2x2 = 0

Solving
-1 + -13x + 2x2 = 0

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

Divide each side by '2'.
-0.5 + -6.5x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -6.5x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -6.5x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -6.5x + x2 = 0 + 0.5
-6.5x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-6.5x + x2 = 0.5

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = 0.5 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 0.5 + 10.5625

Combine like terms: 0.5 + 10.5625 = 11.0625
10.5625 + -6.5x + x2 = 11.0625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 11.0625

Calculate the square root of the right side: 3.326033674

Break this problem into two subproblems by setting 
(x + -3.25) equal to 3.326033674 and -3.326033674.


Subproblem 1
x + -3.25 = 3.326033674

Simplifying
x + -3.25 = 3.326033674

Reorder the terms:
-3.25 + x = 3.326033674

Solving
-3.25 + x = 3.326033674

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = 3.326033674 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 3.326033674 + 3.25
x = 3.326033674 + 3.25

Combine like terms: 3.326033674 + 3.25 = 6.576033674
x = 6.576033674

Simplifying
x = 6.576033674


Subproblem 2
x + -3.25 = -3.326033674

Simplifying
x + -3.25 = -3.326033674

Reorder the terms:
-3.25 + x = -3.326033674

Solving
-3.25 + x = -3.326033674

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = -3.326033674 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -3.326033674 + 3.25
x = -3.326033674 + 3.25

Combine like terms: -3.326033674 + 3.25 = -0.076033674
x = -0.076033674

Simplifying
x = -0.076033674


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.576033674, -0.076033674}
Solution
x = {6.576033674, -0.076033674}

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