3x^2-18x-14=0

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Solution for 3x^2-18x-14=0 equation: 


Simplifying
3x2 + -18x + -14 = 0

Reorder the terms:
-14 + -18x + 3x2 = 0

Solving
-14 + -18x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-4.666666667 + -6x + x2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + -6x + 4.666666667 + x2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + -6x + x2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + -6x + x2 = 0 + 4.666666667
-6x + x2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
-6x + x2 = 4.666666667

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 4.666666667 + 9

Reorder the terms:
9 + -6x + x2 = 4.666666667 + 9

Combine like terms: 4.666666667 + 9 = 13.666666667
9 + -6x + x2 = 13.666666667

Factor a perfect square on the left side:
(x + -3)(x + -3) = 13.666666667

Calculate the square root of the right side: 3.696845502

Break this problem into two subproblems by setting 
(x + -3) equal to 3.696845502 and -3.696845502.


Subproblem 1
x + -3 = 3.696845502

Simplifying
x + -3 = 3.696845502

Reorder the terms:
-3 + x = 3.696845502

Solving
-3 + x = 3.696845502

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 3.696845502 + 3

Combine like terms: -3 + 3 = 0
0 + x = 3.696845502 + 3
x = 3.696845502 + 3

Combine like terms: 3.696845502 + 3 = 6.696845502
x = 6.696845502

Simplifying
x = 6.696845502


Subproblem 2
x + -3 = -3.696845502

Simplifying
x + -3 = -3.696845502

Reorder the terms:
-3 + x = -3.696845502

Solving
-3 + x = -3.696845502

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -3.696845502 + 3

Combine like terms: -3 + 3 = 0
0 + x = -3.696845502 + 3
x = -3.696845502 + 3

Combine like terms: -3.696845502 + 3 = -0.696845502
x = -0.696845502

Simplifying
x = -0.696845502


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.696845502, -0.696845502}

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