-n^2-8n-2=0

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Solution for -n^2-8n-2=0 equation: 


Simplifying
-1n2 + -8n + -2 = 0

Reorder the terms:
-2 + -8n + -1n2 = 0

Solving
-2 + -8n + -1n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 8n + n2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(2 + 8n + n2)' equal to zero and attempt to solve:

Simplifying
2 + 8n + n2 = 0

Solving
2 + 8n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 8n + -2 + n2 = 0 + -2

Reorder the terms:
2 + -2 + 8n + n2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 8n + n2 = 0 + -2
8n + n2 = 0 + -2

Combine like terms: 0 + -2 = -2
8n + n2 = -2

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 = -2 + 16

Reorder the terms:
16 + 8n + n2 = -2 + 16

Combine like terms: -2 + 16 = 14
16 + 8n + n2 = 14

Factor a perfect square on the left side:
(n + 4)(n + 4) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(n + 4) equal to 3.741657387 and -3.741657387.


Subproblem 1
n + 4 = 3.741657387

Simplifying
n + 4 = 3.741657387

Reorder the terms:
4 + n = 3.741657387

Solving
4 + n = 3.741657387

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + n = 3.741657387 + -4

Combine like terms: 4 + -4 = 0
0 + n = 3.741657387 + -4
n = 3.741657387 + -4

Combine like terms: 3.741657387 + -4 = -0.258342613
n = -0.258342613

Simplifying
n = -0.258342613


Subproblem 2
n + 4 = -3.741657387

Simplifying
n + 4 = -3.741657387

Reorder the terms:
4 + n = -3.741657387

Solving
4 + n = -3.741657387

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + n = -3.741657387 + -4

Combine like terms: 4 + -4 = 0
0 + n = -3.741657387 + -4
n = -3.741657387 + -4

Combine like terms: -3.741657387 + -4 = -7.741657387
n = -7.741657387

Simplifying
n = -7.741657387


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.258342613, -7.741657387}
Solution
n = {-0.258342613, -7.741657387}

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