2n^2+9n+45=0

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Solution for 2n^2+9n+45=0 equation:


Simplifying
2n2 + 9n + 45 = 0

Reorder the terms:
45 + 9n + 2n2 = 0

Solving
45 + 9n + 2n2 = 0

Solving for variable 'n'.

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

Divide each side by '2'.
22.5 + 4.5n + n2 = 0

Move the constant term to the right:

Add '-22.5' to each side of the equation.
22.5 + 4.5n + -22.5 + n2 = 0 + -22.5

Reorder the terms:
22.5 + -22.5 + 4.5n + n2 = 0 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + 4.5n + n2 = 0 + -22.5
4.5n + n2 = 0 + -22.5

Combine like terms: 0 + -22.5 = -22.5
4.5n + n2 = -22.5

The n term is 4.5n.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5n + 5.0625 + n2 = -22.5 + 5.0625

Reorder the terms:
5.0625 + 4.5n + n2 = -22.5 + 5.0625

Combine like terms: -22.5 + 5.0625 = -17.4375
5.0625 + 4.5n + n2 = -17.4375

Factor a perfect square on the left side:
(n + 2.25)(n + 2.25) = -17.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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