213-9q+6q^2+q^2+5q-102=0

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Solution for 213-9q+6q^2+q^2+5q-102=0 equation: 


Simplifying
213 + -9q + 6q2 + q2 + 5q + -102 = 0

Reorder the terms:
213 + -102 + -9q + 5q + 6q2 + q2 = 0

Combine like terms: 213 + -102 = 111
111 + -9q + 5q + 6q2 + q2 = 0

Combine like terms: -9q + 5q = -4q
111 + -4q + 6q2 + q2 = 0

Combine like terms: 6q2 + q2 = 7q2
111 + -4q + 7q2 = 0

Solving
111 + -4q + 7q2 = 0

Solving for variable 'q'.

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

Divide each side by '7'.
15.85714286 + -0.5714285714q + q2 = 0

Move the constant term to the right:

Add '-15.85714286' to each side of the equation.
15.85714286 + -0.5714285714q + -15.85714286 + q2 = 0 + -15.85714286

Reorder the terms:
15.85714286 + -15.85714286 + -0.5714285714q + q2 = 0 + -15.85714286

Combine like terms: 15.85714286 + -15.85714286 = 0.00000000
0.00000000 + -0.5714285714q + q2 = 0 + -15.85714286
-0.5714285714q + q2 = 0 + -15.85714286

Combine like terms: 0 + -15.85714286 = -15.85714286
-0.5714285714q + q2 = -15.85714286

The q term is -0.5714285714q.  Take half its coefficient (-0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
-0.5714285714q + 0.08163265305 + q2 = -15.85714286 + 0.08163265305

Reorder the terms:
0.08163265305 + -0.5714285714q + q2 = -15.85714286 + 0.08163265305

Combine like terms: -15.85714286 + 0.08163265305 = -15.77551020695
0.08163265305 + -0.5714285714q + q2 = -15.77551020695

Factor a perfect square on the left side:
(q + -0.2857142857)(q + -0.2857142857) = -15.77551020695

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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