12(x^2)+18x+4=0

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Solution for 12(x^2)+18x+4=0 equation: 


Simplifying
12(x2) + 18x + 4 = 0

Reorder the terms:
4 + 18x + 12x2 = 0

Solving
4 + 18x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 9x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + 9x + 6x2)' equal to zero and attempt to solve:

Simplifying
2 + 9x + 6x2 = 0

Solving
2 + 9x + 6x2 = 0

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

Divide each side by '6'.
0.3333333333 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 1.5x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 1.5x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 1.5x + x2 = 0 + -0.3333333333
1.5x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
1.5x + x2 = -0.3333333333

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = -0.3333333333 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -0.3333333333 + 0.5625

Combine like terms: -0.3333333333 + 0.5625 = 0.2291666667
0.5625 + 1.5x + x2 = 0.2291666667

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 0.2291666667

Calculate the square root of the right side: 0.478713554

Break this problem into two subproblems by setting 
(x + 0.75) equal to 0.478713554 and -0.478713554.


Subproblem 1
x + 0.75 = 0.478713554

Simplifying
x + 0.75 = 0.478713554

Reorder the terms:
0.75 + x = 0.478713554

Solving
0.75 + x = 0.478713554

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 0.478713554 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 0.478713554 + -0.75
x = 0.478713554 + -0.75

Combine like terms: 0.478713554 + -0.75 = -0.271286446
x = -0.271286446

Simplifying
x = -0.271286446


Subproblem 2
x + 0.75 = -0.478713554

Simplifying
x + 0.75 = -0.478713554

Reorder the terms:
0.75 + x = -0.478713554

Solving
0.75 + x = -0.478713554

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -0.478713554 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -0.478713554 + -0.75
x = -0.478713554 + -0.75

Combine like terms: -0.478713554 + -0.75 = -1.228713554
x = -1.228713554

Simplifying
x = -1.228713554


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.271286446, -1.228713554}
Solution
x = {-0.271286446, -1.228713554}

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