n^2+12n+54=0

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Solution for n^2+12n+54=0 equation:


Simplifying
n2 + 12n + 54 = 0

Reorder the terms:
54 + 12n + n2 = 0

Solving
54 + 12n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '-54' to each side of the equation.
54 + 12n + -54 + n2 = 0 + -54

Reorder the terms:
54 + -54 + 12n + n2 = 0 + -54

Combine like terms: 54 + -54 = 0
0 + 12n + n2 = 0 + -54
12n + n2 = 0 + -54

Combine like terms: 0 + -54 = -54
12n + n2 = -54

The n term is 12n.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12n + 36 + n2 = -54 + 36

Reorder the terms:
36 + 12n + n2 = -54 + 36

Combine like terms: -54 + 36 = -18
36 + 12n + n2 = -18

Factor a perfect square on the left side:
(n + 6)(n + 6) = -18

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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