6x^2-18x+2=0

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


Simplifying
6x2 + -18x + 2 = 0

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

Solving
2 + -18x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -9x + 3x2) = 0

Ignore the factor 2.

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

Simplifying
1 + -9x + 3x2 = 0

Solving
1 + -9x + 3x2 = 0

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

Divide each side by '3'.
0.3333333333 + -3x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -3x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -3x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -3x + x2 = 0 + -0.3333333333
-3x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-3x + x2 = -0.3333333333

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 = -0.3333333333 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -0.3333333333 + 2.25

Combine like terms: -0.3333333333 + 2.25 = 1.9166666667
2.25 + -3x + x2 = 1.9166666667

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 1.9166666667

Calculate the square root of the right side: 1.38443731

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.38443731 and -1.38443731.


Subproblem 1
x + -1.5 = 1.38443731

Simplifying
x + -1.5 = 1.38443731

Reorder the terms:
-1.5 + x = 1.38443731

Solving
-1.5 + x = 1.38443731

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 = 1.38443731 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 1.38443731 + 1.5
x = 1.38443731 + 1.5

Combine like terms: 1.38443731 + 1.5 = 2.88443731
x = 2.88443731

Simplifying
x = 2.88443731


Subproblem 2
x + -1.5 = -1.38443731

Simplifying
x + -1.5 = -1.38443731

Reorder the terms:
-1.5 + x = -1.38443731

Solving
-1.5 + x = -1.38443731

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 = -1.38443731 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -1.38443731 + 1.5
x = -1.38443731 + 1.5

Combine like terms: -1.38443731 + 1.5 = 0.11556269
x = 0.11556269

Simplifying
x = 0.11556269


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.88443731, 0.11556269}
Solution
x = {2.88443731, 0.11556269}

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