12x^2-60x-70=0

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Solution for 12x^2-60x-70=0 equation: 


Simplifying
12x2 + -60x + -70 = 0

Reorder the terms:
-70 + -60x + 12x2 = 0

Solving
-70 + -60x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + -30x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-35 + -30x + 6x2)' equal to zero and attempt to solve:

Simplifying
-35 + -30x + 6x2 = 0

Solving
-35 + -30x + 6x2 = 0

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

Divide each side by '6'.
-5.833333333 + -5x + x2 = 0

Move the constant term to the right:

Add '5.833333333' to each side of the equation.
-5.833333333 + -5x + 5.833333333 + x2 = 0 + 5.833333333

Reorder the terms:
-5.833333333 + 5.833333333 + -5x + x2 = 0 + 5.833333333

Combine like terms: -5.833333333 + 5.833333333 = 0.000000000
0.000000000 + -5x + x2 = 0 + 5.833333333
-5x + x2 = 0 + 5.833333333

Combine like terms: 0 + 5.833333333 = 5.833333333
-5x + x2 = 5.833333333

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 5.833333333 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 5.833333333 + 6.25

Combine like terms: 5.833333333 + 6.25 = 12.083333333
6.25 + -5x + x2 = 12.083333333

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 12.083333333

Calculate the square root of the right side: 3.476108936

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.476108936 and -3.476108936.


Subproblem 1
x + -2.5 = 3.476108936

Simplifying
x + -2.5 = 3.476108936

Reorder the terms:
-2.5 + x = 3.476108936

Solving
-2.5 + x = 3.476108936

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 3.476108936 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 3.476108936 + 2.5
x = 3.476108936 + 2.5

Combine like terms: 3.476108936 + 2.5 = 5.976108936
x = 5.976108936

Simplifying
x = 5.976108936


Subproblem 2
x + -2.5 = -3.476108936

Simplifying
x + -2.5 = -3.476108936

Reorder the terms:
-2.5 + x = -3.476108936

Solving
-2.5 + x = -3.476108936

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -3.476108936 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -3.476108936 + 2.5
x = -3.476108936 + 2.5

Combine like terms: -3.476108936 + 2.5 = -0.976108936
x = -0.976108936

Simplifying
x = -0.976108936


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.976108936, -0.976108936}
Solution
x = {5.976108936, -0.976108936}

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