21n^2+7n+14=11

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Solution for 21n^2+7n+14=11 equation: 


Simplifying
21n2 + 7n + 14 = 11

Reorder the terms:
14 + 7n + 21n2 = 11

Solving
14 + 7n + 21n2 = 11

Solving for variable 'n'.

Reorder the terms:
14 + -11 + 7n + 21n2 = 11 + -11

Combine like terms: 14 + -11 = 3
3 + 7n + 21n2 = 11 + -11

Combine like terms: 11 + -11 = 0
3 + 7n + 21n2 = 0

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

Divide each side by '21'.
0.1428571429 + 0.3333333333n + n2 = 0

Move the constant term to the right:

Add '-0.1428571429' to each side of the equation.
0.1428571429 + 0.3333333333n + -0.1428571429 + n2 = 0 + -0.1428571429

Reorder the terms:
0.1428571429 + -0.1428571429 + 0.3333333333n + n2 = 0 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + 0.3333333333n + n2 = 0 + -0.1428571429
0.3333333333n + n2 = 0 + -0.1428571429

Combine like terms: 0 + -0.1428571429 = -0.1428571429
0.3333333333n + n2 = -0.1428571429

The n term is 0.3333333333n.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333n + 0.02777777779 + n2 = -0.1428571429 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333n + n2 = -0.1428571429 + 0.02777777779

Combine like terms: -0.1428571429 + 0.02777777779 = -0.11507936511
0.02777777779 + 0.3333333333n + n2 = -0.11507936511

Factor a perfect square on the left side:
(n + 0.1666666667)(n + 0.1666666667) = -0.11507936511

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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