12x^2+18x+2=0

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


Simplifying
12x2 + 18x + 2 = 0

Reorder the terms:
2 + 18x + 12x2 = 0

Solving
2 + 18x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 9x + 6x2) = 0

Ignore the factor 2.

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

Simplifying
1 + 9x + 6x2 = 0

Solving
1 + 9x + 6x2 = 0

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

Divide each side by '6'.
0.1666666667 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 1.5x + -0.1666666667 + x2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 1.5x + x2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 1.5x + x2 = 0 + -0.1666666667
1.5x + x2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
1.5x + x2 = -0.1666666667

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 = -0.1666666667 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -0.1666666667 + 0.5625

Combine like terms: -0.1666666667 + 0.5625 = 0.3958333333
0.5625 + 1.5x + x2 = 0.3958333333

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 0.3958333333

Calculate the square root of the right side: 0.62915287

Break this problem into two subproblems by setting 
(x + 0.75) equal to 0.62915287 and -0.62915287.


Subproblem 1
x + 0.75 = 0.62915287

Simplifying
x + 0.75 = 0.62915287

Reorder the terms:
0.75 + x = 0.62915287

Solving
0.75 + x = 0.62915287

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 = 0.62915287 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 0.62915287 + -0.75
x = 0.62915287 + -0.75

Combine like terms: 0.62915287 + -0.75 = -0.12084713
x = -0.12084713

Simplifying
x = -0.12084713


Subproblem 2
x + 0.75 = -0.62915287

Simplifying
x + 0.75 = -0.62915287

Reorder the terms:
0.75 + x = -0.62915287

Solving
0.75 + x = -0.62915287

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 = -0.62915287 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -0.62915287 + -0.75
x = -0.62915287 + -0.75

Combine like terms: -0.62915287 + -0.75 = -1.37915287
x = -1.37915287

Simplifying
x = -1.37915287


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.12084713, -1.37915287}
Solution
x = {-0.12084713, -1.37915287}

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