9x^2-27x+21=0

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Solution for 9x^2-27x+21=0 equation: 


Simplifying
9x2 + -27x + 21 = 0

Reorder the terms:
21 + -27x + 9x2 = 0

Solving
21 + -27x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + -9x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(7 + -9x + 3x2)' equal to zero and attempt to solve:

Simplifying
7 + -9x + 3x2 = 0

Solving
7 + -9x + 3x2 = 0

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

Divide each side by '3'.
2.333333333 + -3x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -3x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -3x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -3x + x2 = 0 + -2.333333333
-3x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-3x + x2 = -2.333333333

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 = -2.333333333 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -2.333333333 + 2.25

Combine like terms: -2.333333333 + 2.25 = -0.083333333
2.25 + -3x + x2 = -0.083333333

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -0.083333333

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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