6n^2+n+8=0

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Solution for 6n^2+n+8=0 equation:


Simplifying
6n2 + n + 8 = 0

Reorder the terms:
8 + n + 6n2 = 0

Solving
8 + n + 6n2 = 0

Solving for variable 'n'.

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

Divide each side by '6'.
1.333333333 + 0.1666666667n + n2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 0.1666666667n + -1.333333333 + n2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 0.1666666667n + n2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 0.1666666667n + n2 = 0 + -1.333333333
0.1666666667n + n2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
0.1666666667n + n2 = -1.333333333

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1666666667n + 0.25 + n2 = -1.333333333 + 0.25

Reorder the terms:
0.25 + 0.1666666667n + n2 = -1.333333333 + 0.25

Combine like terms: -1.333333333 + 0.25 = -1.083333333
0.25 + 0.1666666667n + n2 = -1.083333333

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -1.083333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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