6x^2-18x-14=0

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Solution for 6x^2-18x-14=0 equation: 


Simplifying
6x2 + -18x + -14 = 0

Reorder the terms:
-14 + -18x + 6x2 = 0

Solving
-14 + -18x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -9x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -9x + 3x2)' equal to zero and attempt to solve:

Simplifying
-7 + -9x + 3x2 = 0

Solving
-7 + -9x + 3x2 = 0

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

Divide each side by '3'.
-2.333333333 + -3x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -3x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -3x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -3x + x2 = 0 + 2.333333333
-3x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-3x + x2 = 2.333333333

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 2.333333333 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 2.333333333 + 2.25

Combine like terms: 2.333333333 + 2.25 = 4.583333333
2.25 + -3x + x2 = 4.583333333

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 4.583333333

Calculate the square root of the right side: 2.140872096

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.140872096 and -2.140872096.


Subproblem 1
x + -1.5 = 2.140872096

Simplifying
x + -1.5 = 2.140872096

Reorder the terms:
-1.5 + x = 2.140872096

Solving
-1.5 + x = 2.140872096

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 2.140872096 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.140872096 + 1.5
x = 2.140872096 + 1.5

Combine like terms: 2.140872096 + 1.5 = 3.640872096
x = 3.640872096

Simplifying
x = 3.640872096


Subproblem 2
x + -1.5 = -2.140872096

Simplifying
x + -1.5 = -2.140872096

Reorder the terms:
-1.5 + x = -2.140872096

Solving
-1.5 + x = -2.140872096

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -2.140872096 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.140872096 + 1.5
x = -2.140872096 + 1.5

Combine like terms: -2.140872096 + 1.5 = -0.640872096
x = -0.640872096

Simplifying
x = -0.640872096


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.640872096, -0.640872096}
Solution
x = {3.640872096, -0.640872096}

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