9Q^2-54Q+120=

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Solution for 9Q^2-54Q+120= equation: 


Simplifying
9Q2 + -54Q + 120 = 0

Reorder the terms:
120 + -54Q + 9Q2 = 0

Solving
120 + -54Q + 9Q2 = 0

Solving for variable 'Q'.

Factor out the Greatest Common Factor (GCF), '3'.
3(40 + -18Q + 3Q2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(40 + -18Q + 3Q2)' equal to zero and attempt to solve:

Simplifying
40 + -18Q + 3Q2 = 0

Solving
40 + -18Q + 3Q2 = 0

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

Divide each side by '3'.
13.33333333 + -6Q + Q2 = 0

Move the constant term to the right:

Add '-13.33333333' to each side of the equation.
13.33333333 + -6Q + -13.33333333 + Q2 = 0 + -13.33333333

Reorder the terms:
13.33333333 + -13.33333333 + -6Q + Q2 = 0 + -13.33333333

Combine like terms: 13.33333333 + -13.33333333 = 0.00000000
0.00000000 + -6Q + Q2 = 0 + -13.33333333
-6Q + Q2 = 0 + -13.33333333

Combine like terms: 0 + -13.33333333 = -13.33333333
-6Q + Q2 = -13.33333333

The Q term is -6Q.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6Q + 9 + Q2 = -13.33333333 + 9

Reorder the terms:
9 + -6Q + Q2 = -13.33333333 + 9

Combine like terms: -13.33333333 + 9 = -4.33333333
9 + -6Q + Q2 = -4.33333333

Factor a perfect square on the left side:
(Q + -3)(Q + -3) = -4.33333333

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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