9x^2-81x+162+60=0

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Solution for 9x^2-81x+162+60=0 equation: 


Simplifying
9x2 + -81x + 162 + 60 = 0

Reorder the terms:
162 + 60 + -81x + 9x2 = 0

Combine like terms: 162 + 60 = 222
222 + -81x + 9x2 = 0

Solving
222 + -81x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(74 + -27x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(74 + -27x + 3x2)' equal to zero and attempt to solve:

Simplifying
74 + -27x + 3x2 = 0

Solving
74 + -27x + 3x2 = 0

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

Divide each side by '3'.
24.66666667 + -9x + x2 = 0

Move the constant term to the right:

Add '-24.66666667' to each side of the equation.
24.66666667 + -9x + -24.66666667 + x2 = 0 + -24.66666667

Reorder the terms:
24.66666667 + -24.66666667 + -9x + x2 = 0 + -24.66666667

Combine like terms: 24.66666667 + -24.66666667 = 0.00000000
0.00000000 + -9x + x2 = 0 + -24.66666667
-9x + x2 = 0 + -24.66666667

Combine like terms: 0 + -24.66666667 = -24.66666667
-9x + x2 = -24.66666667

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -24.66666667 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -24.66666667 + 20.25

Combine like terms: -24.66666667 + 20.25 = -4.41666667
20.25 + -9x + x2 = -4.41666667

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = -4.41666667

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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