(12x^2)+18x-14=0

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Solution for (12x^2)+18x-14=0 equation: 


Simplifying
(12x2) + 18x + -14 = 0

Reorder the terms:
-14 + 18x + (12x2) = 0

Solving
-14 + 18x + (12x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 9x + (6x2)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + 9x + (6x2))' equal to zero and attempt to solve:

Simplifying
-7 + 9x + (6x2) = 0

Solving
-7 + 9x + (6x2) = 0

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

Divide each side by '6'.
-1.166666667 + 1.5x + x2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.5x + 1.166666667 + x2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + 1.5x + x2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + 1.5x + x2 = 0 + 1.166666667
1.5x + x2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
1.5x + x2 = 1.166666667

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 = 1.166666667 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 1.166666667 + 0.5625

Combine like terms: 1.166666667 + 0.5625 = 1.729166667
0.5625 + 1.5x + x2 = 1.729166667

Factor a perfect square on the left side:
((x) + 0.75)((x) + 0.75) = 1.729166667

Calculate the square root of the right side: 1.31497782

Break this problem into two subproblems by setting 
((x) + 0.75) equal to 1.31497782 and -1.31497782.


Subproblem 1
(x) + 0.75 = 1.31497782

Simplifying
(x) + 0.75 = 1.31497782
x + 0.75 = 1.31497782

Reorder the terms:
0.75 + x = 1.31497782

Solving
0.75 + x = 1.31497782

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 = 1.31497782 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 1.31497782 + -0.75
x = 1.31497782 + -0.75

Combine like terms: 1.31497782 + -0.75 = 0.56497782
x = 0.56497782

Simplifying
x = 0.56497782


Subproblem 2
(x) + 0.75 = -1.31497782

Simplifying
(x) + 0.75 = -1.31497782
x + 0.75 = -1.31497782

Reorder the terms:
0.75 + x = -1.31497782

Solving
0.75 + x = -1.31497782

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 = -1.31497782 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -1.31497782 + -0.75
x = -1.31497782 + -0.75

Combine like terms: -1.31497782 + -0.75 = -2.06497782
x = -2.06497782

Simplifying
x = -2.06497782


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.56497782, -2.06497782}
Solution
x = {0.56497782, -2.06497782}

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