2(q^2+20)+17q=-10q^2

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Solution for 2(q^2+20)+17q=-10q^2 equation: 


Simplifying
2(q2 + 20) + 17q = -10q2

Reorder the terms:
2(20 + q2) + 17q = -10q2
(20 * 2 + q2 * 2) + 17q = -10q2
(40 + 2q2) + 17q = -10q2

Reorder the terms:
40 + 17q + 2q2 = -10q2

Solving
40 + 17q + 2q2 = -10q2

Solving for variable 'q'.

Combine like terms: 2q2 + 10q2 = 12q2
40 + 17q + 12q2 = -10q2 + 10q2

Combine like terms: -10q2 + 10q2 = 0
40 + 17q + 12q2 = 0

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

Divide each side by '12'.
3.333333333 + 1.416666667q + q2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + 1.416666667q + -3.333333333 + q2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + 1.416666667q + q2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + 1.416666667q + q2 = 0 + -3.333333333
1.416666667q + q2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
1.416666667q + q2 = -3.333333333

The q term is 1.416666667q.  Take half its coefficient (0.7083333335).
Square it (0.5017361113) and add it to both sides.

Add '0.5017361113' to each side of the equation.
1.416666667q + 0.5017361113 + q2 = -3.333333333 + 0.5017361113

Reorder the terms:
0.5017361113 + 1.416666667q + q2 = -3.333333333 + 0.5017361113

Combine like terms: -3.333333333 + 0.5017361113 = -2.8315972217
0.5017361113 + 1.416666667q + q2 = -2.8315972217

Factor a perfect square on the left side:
(q + 0.7083333335)(q + 0.7083333335) = -2.8315972217

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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