2x^2-18x-6=0

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


Simplifying
2x2 + -18x + -6 = 0

Reorder the terms:
-6 + -18x + 2x2 = 0

Solving
-6 + -18x + 2x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.

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

Simplifying
-3 + -9x + x2 = 0

Solving
-3 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -9x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -9x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -9x + x2 = 0 + 3
-9x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-9x + x2 = 3

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 3 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 3 + 20.25

Combine like terms: 3 + 20.25 = 23.25
20.25 + -9x + x2 = 23.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 23.25

Calculate the square root of the right side: 4.82182538

Break this problem into two subproblems by setting 
(x + -4.5) equal to 4.82182538 and -4.82182538.


Subproblem 1
x + -4.5 = 4.82182538

Simplifying
x + -4.5 = 4.82182538

Reorder the terms:
-4.5 + x = 4.82182538

Solving
-4.5 + x = 4.82182538

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 4.82182538 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 4.82182538 + 4.5
x = 4.82182538 + 4.5

Combine like terms: 4.82182538 + 4.5 = 9.32182538
x = 9.32182538

Simplifying
x = 9.32182538


Subproblem 2
x + -4.5 = -4.82182538

Simplifying
x + -4.5 = -4.82182538

Reorder the terms:
-4.5 + x = -4.82182538

Solving
-4.5 + x = -4.82182538

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -4.82182538 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -4.82182538 + 4.5
x = -4.82182538 + 4.5

Combine like terms: -4.82182538 + 4.5 = -0.32182538
x = -0.32182538

Simplifying
x = -0.32182538


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.32182538, -0.32182538}
Solution
x = {9.32182538, -0.32182538}

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