12x^2-7x-9=0

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Solution for 12x^2-7x-9=0 equation: 


Simplifying
12x2 + -7x + -9 = 0

Reorder the terms:
-9 + -7x + 12x2 = 0

Solving
-9 + -7x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
-0.75 + -0.5833333333x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -0.5833333333x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -0.5833333333x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -0.5833333333x + x2 = 0 + 0.75
-0.5833333333x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-0.5833333333x + x2 = 0.75

The x term is -0.5833333333x.  Take half its coefficient (-0.2916666667).
Square it (0.08506944446) and add it to both sides.

Add '0.08506944446' to each side of the equation.
-0.5833333333x + 0.08506944446 + x2 = 0.75 + 0.08506944446

Reorder the terms:
0.08506944446 + -0.5833333333x + x2 = 0.75 + 0.08506944446

Combine like terms: 0.75 + 0.08506944446 = 0.83506944446
0.08506944446 + -0.5833333333x + x2 = 0.83506944446

Factor a perfect square on the left side:
(x + -0.2916666667)(x + -0.2916666667) = 0.83506944446

Calculate the square root of the right side: 0.913821342

Break this problem into two subproblems by setting 
(x + -0.2916666667) equal to 0.913821342 and -0.913821342.


Subproblem 1
x + -0.2916666667 = 0.913821342

Simplifying
x + -0.2916666667 = 0.913821342

Reorder the terms:
-0.2916666667 + x = 0.913821342

Solving
-0.2916666667 + x = 0.913821342

Solving for variable 'x'.

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

Add '0.2916666667' to each side of the equation.
-0.2916666667 + 0.2916666667 + x = 0.913821342 + 0.2916666667

Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000
0.0000000000 + x = 0.913821342 + 0.2916666667
x = 0.913821342 + 0.2916666667

Combine like terms: 0.913821342 + 0.2916666667 = 1.2054880087
x = 1.2054880087

Simplifying
x = 1.2054880087


Subproblem 2
x + -0.2916666667 = -0.913821342

Simplifying
x + -0.2916666667 = -0.913821342

Reorder the terms:
-0.2916666667 + x = -0.913821342

Solving
-0.2916666667 + x = -0.913821342

Solving for variable 'x'.

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

Add '0.2916666667' to each side of the equation.
-0.2916666667 + 0.2916666667 + x = -0.913821342 + 0.2916666667

Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000
0.0000000000 + x = -0.913821342 + 0.2916666667
x = -0.913821342 + 0.2916666667

Combine like terms: -0.913821342 + 0.2916666667 = -0.6221546753
x = -0.6221546753

Simplifying
x = -0.6221546753


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2054880087, -0.6221546753}

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