n^2=-8n-39

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Solution for n^2=-8n-39 equation:


Simplifying
n2 = -8n + -39

Reorder the terms:
n2 = -39 + -8n

Solving
n2 = -39 + -8n

Solving for variable 'n'.

Reorder the terms:
39 + 8n + n2 = -39 + -8n + 39 + 8n

Reorder the terms:
39 + 8n + n2 = -39 + 39 + -8n + 8n

Combine like terms: -39 + 39 = 0
39 + 8n + n2 = 0 + -8n + 8n
39 + 8n + n2 = -8n + 8n

Combine like terms: -8n + 8n = 0
39 + 8n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-39' to each side of the equation.
39 + 8n + -39 + n2 = 0 + -39

Reorder the terms:
39 + -39 + 8n + n2 = 0 + -39

Combine like terms: 39 + -39 = 0
0 + 8n + n2 = 0 + -39
8n + n2 = 0 + -39

Combine like terms: 0 + -39 = -39
8n + n2 = -39

The n term is 8n.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8n + 16 + n2 = -39 + 16

Reorder the terms:
16 + 8n + n2 = -39 + 16

Combine like terms: -39 + 16 = -23
16 + 8n + n2 = -23

Factor a perfect square on the left side:
(n + 4)(n + 4) = -23

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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