12x^2+4x-9=0

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Solution for 12x^2+4x-9=0 equation: 


Simplifying
12x2 + 4x + -9 = 0

Reorder the terms:
-9 + 4x + 12x2 = 0

Solving
-9 + 4x + 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 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 0.3333333333x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 0.3333333333x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 0.3333333333x + x2 = 0 + 0.75
0.3333333333x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
0.3333333333x + x2 = 0.75

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = 0.75 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = 0.75 + 0.02777777779

Combine like terms: 0.75 + 0.02777777779 = 0.77777777779
0.02777777779 + 0.3333333333x + x2 = 0.77777777779

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = 0.77777777779

Calculate the square root of the right side: 0.881917104

Break this problem into two subproblems by setting 
(x + 0.1666666667) equal to 0.881917104 and -0.881917104.


Subproblem 1
x + 0.1666666667 = 0.881917104

Simplifying
x + 0.1666666667 = 0.881917104

Reorder the terms:
0.1666666667 + x = 0.881917104

Solving
0.1666666667 + x = 0.881917104

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = 0.881917104 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = 0.881917104 + -0.1666666667
x = 0.881917104 + -0.1666666667

Combine like terms: 0.881917104 + -0.1666666667 = 0.7152504373
x = 0.7152504373

Simplifying
x = 0.7152504373


Subproblem 2
x + 0.1666666667 = -0.881917104

Simplifying
x + 0.1666666667 = -0.881917104

Reorder the terms:
0.1666666667 + x = -0.881917104

Solving
0.1666666667 + x = -0.881917104

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = -0.881917104 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = -0.881917104 + -0.1666666667
x = -0.881917104 + -0.1666666667

Combine like terms: -0.881917104 + -0.1666666667 = -1.0485837707
x = -1.0485837707

Simplifying
x = -1.0485837707


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7152504373, -1.0485837707}

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