3q^2+11=5q

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Solution for 3q^2+11=5q equation:


Simplifying
3q2 + 11 = 5q

Reorder the terms:
11 + 3q2 = 5q

Solving
11 + 3q2 = 5q

Solving for variable 'q'.

Reorder the terms:
11 + -5q + 3q2 = 5q + -5q

Combine like terms: 5q + -5q = 0
11 + -5q + 3q2 = 0

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

Divide each side by '3'.
3.666666667 + -1.666666667q + q2 = 0

Move the constant term to the right:

Add '-3.666666667' to each side of the equation.
3.666666667 + -1.666666667q + -3.666666667 + q2 = 0 + -3.666666667

Reorder the terms:
3.666666667 + -3.666666667 + -1.666666667q + q2 = 0 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + -1.666666667q + q2 = 0 + -3.666666667
-1.666666667q + q2 = 0 + -3.666666667

Combine like terms: 0 + -3.666666667 = -3.666666667
-1.666666667q + q2 = -3.666666667

The q term is -1.666666667q.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667q + 0.6944444447 + q2 = -3.666666667 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667q + q2 = -3.666666667 + 0.6944444447

Combine like terms: -3.666666667 + 0.6944444447 = -2.9722222223
0.6944444447 + -1.666666667q + q2 = -2.9722222223

Factor a perfect square on the left side:
(q + -0.8333333335)(q + -0.8333333335) = -2.9722222223

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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