n^2+15n+57=0

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Solution for n^2+15n+57=0 equation:


Simplifying
n2 + 15n + 57 = 0

Reorder the terms:
57 + 15n + n2 = 0

Solving
57 + 15n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '-57' to each side of the equation.
57 + 15n + -57 + n2 = 0 + -57

Reorder the terms:
57 + -57 + 15n + n2 = 0 + -57

Combine like terms: 57 + -57 = 0
0 + 15n + n2 = 0 + -57
15n + n2 = 0 + -57

Combine like terms: 0 + -57 = -57
15n + n2 = -57

The n term is 15n.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15n + 56.25 + n2 = -57 + 56.25

Reorder the terms:
56.25 + 15n + n2 = -57 + 56.25

Combine like terms: -57 + 56.25 = -0.75
56.25 + 15n + n2 = -0.75

Factor a perfect square on the left side:
(n + 7.5)(n + 7.5) = -0.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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