12x^2-8x-7-7=

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Solution for 12x^2-8x-7-7= equation: 


Simplifying
12x2 + -8x + -7 + -7 = 0

Reorder the terms:
-7 + -7 + -8x + 12x2 = 0

Combine like terms: -7 + -7 = -14
-14 + -8x + 12x2 = 0

Solving
-14 + -8x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -4x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -4x + 6x2)' equal to zero and attempt to solve:

Simplifying
-7 + -4x + 6x2 = 0

Solving
-7 + -4x + 6x2 = 0

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

Divide each side by '6'.
-1.166666667 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + -0.6666666667x + 1.166666667 + x2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + -0.6666666667x + x2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + -0.6666666667x + x2 = 0 + 1.166666667
-0.6666666667x + x2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
-0.6666666667x + x2 = 1.166666667

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 1.166666667 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 1.166666667 + 0.1111111112

Combine like terms: 1.166666667 + 0.1111111112 = 1.2777777782
0.1111111112 + -0.6666666667x + x2 = 1.2777777782

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 1.2777777782

Calculate the square root of the right side: 1.130388331

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 1.130388331 and -1.130388331.


Subproblem 1
x + -0.3333333334 = 1.130388331

Simplifying
x + -0.3333333334 = 1.130388331

Reorder the terms:
-0.3333333334 + x = 1.130388331

Solving
-0.3333333334 + x = 1.130388331

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 1.130388331 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 1.130388331 + 0.3333333334
x = 1.130388331 + 0.3333333334

Combine like terms: 1.130388331 + 0.3333333334 = 1.4637216644
x = 1.4637216644

Simplifying
x = 1.4637216644


Subproblem 2
x + -0.3333333334 = -1.130388331

Simplifying
x + -0.3333333334 = -1.130388331

Reorder the terms:
-0.3333333334 + x = -1.130388331

Solving
-0.3333333334 + x = -1.130388331

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -1.130388331 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -1.130388331 + 0.3333333334
x = -1.130388331 + 0.3333333334

Combine like terms: -1.130388331 + 0.3333333334 = -0.7970549976
x = -0.7970549976

Simplifying
x = -0.7970549976


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.4637216644, -0.7970549976}
Solution
x = {1.4637216644, -0.7970549976}

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