12x^2-68x-30=0

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Solution for 12x^2-68x-30=0 equation: 


Simplifying
12x2 + -68x + -30 = 0

Reorder the terms:
-30 + -68x + 12x2 = 0

Solving
-30 + -68x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -34x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + -34x + 6x2)' equal to zero and attempt to solve:

Simplifying
-15 + -34x + 6x2 = 0

Solving
-15 + -34x + 6x2 = 0

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

Divide each side by '6'.
-2.5 + -5.666666667x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -5.666666667x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -5.666666667x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -5.666666667x + x2 = 0 + 2.5
-5.666666667x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-5.666666667x + x2 = 2.5

The x term is -5.666666667x.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667x + 8.027777782 + x2 = 2.5 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667x + x2 = 2.5 + 8.027777782

Combine like terms: 2.5 + 8.027777782 = 10.527777782
8.027777782 + -5.666666667x + x2 = 10.527777782

Factor a perfect square on the left side:
(x + -2.833333334)(x + -2.833333334) = 10.527777782

Calculate the square root of the right side: 3.244653723

Break this problem into two subproblems by setting 
(x + -2.833333334) equal to 3.244653723 and -3.244653723.


Subproblem 1
x + -2.833333334 = 3.244653723

Simplifying
x + -2.833333334 = 3.244653723

Reorder the terms:
-2.833333334 + x = 3.244653723

Solving
-2.833333334 + x = 3.244653723

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = 3.244653723 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = 3.244653723 + 2.833333334
x = 3.244653723 + 2.833333334

Combine like terms: 3.244653723 + 2.833333334 = 6.077987057
x = 6.077987057

Simplifying
x = 6.077987057


Subproblem 2
x + -2.833333334 = -3.244653723

Simplifying
x + -2.833333334 = -3.244653723

Reorder the terms:
-2.833333334 + x = -3.244653723

Solving
-2.833333334 + x = -3.244653723

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = -3.244653723 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = -3.244653723 + 2.833333334
x = -3.244653723 + 2.833333334

Combine like terms: -3.244653723 + 2.833333334 = -0.411320389
x = -0.411320389

Simplifying
x = -0.411320389


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.077987057, -0.411320389}
Solution
x = {6.077987057, -0.411320389}

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