9x^2-6x+6=0

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Solution for 9x^2-6x+6=0 equation:


Simplifying
9x2 + -6x + 6 = 0

Reorder the terms:
6 + -6x + 9x2 = 0

Solving
6 + -6x + 9x2 = 0

Solving for variable 'x'.

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

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + -2x + 3x2)' equal to zero and attempt to solve:

Simplifying
2 + -2x + 3x2 = 0

Solving
2 + -2x + 3x2 = 0

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

Divide each side by '3'.
0.6666666667 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -0.6666666667x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -0.6666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -0.6666666667x + x2 = 0 + -0.6666666667
-0.6666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-0.6666666667x + x2 = -0.6666666667

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = -0.6666666667 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = -0.6666666667 + 0.1111111112

Combine like terms: -0.6666666667 + 0.1111111112 = -0.5555555555
0.1111111112 + -0.6666666667x + x2 = -0.5555555555

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = -0.5555555555

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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