3n^2+11n+38=0

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Solution for 3n^2+11n+38=0 equation: 


Simplifying
3n2 + 11n + 38 = 0

Reorder the terms:
38 + 11n + 3n2 = 0

Solving
38 + 11n + 3n2 = 0

Solving for variable 'n'.

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

Divide each side by '3'.
12.66666667 + 3.666666667n + n2 = 0

Move the constant term to the right:

Add '-12.66666667' to each side of the equation.
12.66666667 + 3.666666667n + -12.66666667 + n2 = 0 + -12.66666667

Reorder the terms:
12.66666667 + -12.66666667 + 3.666666667n + n2 = 0 + -12.66666667

Combine like terms: 12.66666667 + -12.66666667 = 0.00000000
0.00000000 + 3.666666667n + n2 = 0 + -12.66666667
3.666666667n + n2 = 0 + -12.66666667

Combine like terms: 0 + -12.66666667 = -12.66666667
3.666666667n + n2 = -12.66666667

The n term is 3.666666667n.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667n + 3.361111114 + n2 = -12.66666667 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667n + n2 = -12.66666667 + 3.361111114

Combine like terms: -12.66666667 + 3.361111114 = -9.305555556
3.361111114 + 3.666666667n + n2 = -9.305555556

Factor a perfect square on the left side:
(n + 1.833333334)(n + 1.833333334) = -9.305555556

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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