27x^2-72x+192=0

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Solution for 27x^2-72x+192=0 equation: 


Simplifying
27x2 + -72x + 192 = 0

Reorder the terms:
192 + -72x + 27x2 = 0

Solving
192 + -72x + 27x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(64 + -24x + 9x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(64 + -24x + 9x2)' equal to zero and attempt to solve:

Simplifying
64 + -24x + 9x2 = 0

Solving
64 + -24x + 9x2 = 0

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

Divide each side by '9'.
7.111111111 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '-7.111111111' to each side of the equation.
7.111111111 + -2.666666667x + -7.111111111 + x2 = 0 + -7.111111111

Reorder the terms:
7.111111111 + -7.111111111 + -2.666666667x + x2 = 0 + -7.111111111

Combine like terms: 7.111111111 + -7.111111111 = 0.000000000
0.000000000 + -2.666666667x + x2 = 0 + -7.111111111
-2.666666667x + x2 = 0 + -7.111111111

Combine like terms: 0 + -7.111111111 = -7.111111111
-2.666666667x + x2 = -7.111111111

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = -7.111111111 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = -7.111111111 + 1.777777780

Combine like terms: -7.111111111 + 1.777777780 = -5.333333331
1.777777780 + -2.666666667x + x2 = -5.333333331

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = -5.333333331

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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