6x^2-18x+81=0

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Solution for 6x^2-18x+81=0 equation: 


Simplifying
6x2 + -18x + 81 = 0

Reorder the terms:
81 + -18x + 6x2 = 0

Solving
81 + -18x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(27 + -6x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(27 + -6x + 2x2)' equal to zero and attempt to solve:

Simplifying
27 + -6x + 2x2 = 0

Solving
27 + -6x + 2x2 = 0

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

Divide each side by '2'.
13.5 + -3x + x2 = 0

Move the constant term to the right:

Add '-13.5' to each side of the equation.
13.5 + -3x + -13.5 + x2 = 0 + -13.5

Reorder the terms:
13.5 + -13.5 + -3x + x2 = 0 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + -3x + x2 = 0 + -13.5
-3x + x2 = 0 + -13.5

Combine like terms: 0 + -13.5 = -13.5
-3x + x2 = -13.5

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 = -13.5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -13.5 + 2.25

Combine like terms: -13.5 + 2.25 = -11.25
2.25 + -3x + x2 = -11.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -11.25

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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