3q^2-16q+57=0

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Solution for 3q^2-16q+57=0 equation:


Simplifying
3q2 + -16q + 57 = 0

Reorder the terms:
57 + -16q + 3q2 = 0

Solving
57 + -16q + 3q2 = 0

Solving for variable 'q'.

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

Divide each side by '3'.
19 + -5.333333333q + q2 = 0

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + -5.333333333q + -19 + q2 = 0 + -19

Reorder the terms:
19 + -19 + -5.333333333q + q2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -5.333333333q + q2 = 0 + -19
-5.333333333q + q2 = 0 + -19

Combine like terms: 0 + -19 = -19
-5.333333333q + q2 = -19

The q term is -5.333333333q.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333q + 7.111111113 + q2 = -19 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333q + q2 = -19 + 7.111111113

Combine like terms: -19 + 7.111111113 = -11.888888887
7.111111113 + -5.333333333q + q2 = -11.888888887

Factor a perfect square on the left side:
(q + -2.666666667)(q + -2.666666667) = -11.888888887

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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