n^2-8n-36=-6

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Solution for n^2-8n-36=-6 equation: 


Simplifying
n2 + -8n + -36 = -6

Reorder the terms:
-36 + -8n + n2 = -6

Solving
-36 + -8n + n2 = -6

Solving for variable 'n'.

Reorder the terms:
-36 + 6 + -8n + n2 = -6 + 6

Combine like terms: -36 + 6 = -30
-30 + -8n + n2 = -6 + 6

Combine like terms: -6 + 6 = 0
-30 + -8n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -8n + 30 + n2 = 0 + 30

Reorder the terms:
-30 + 30 + -8n + n2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -8n + n2 = 0 + 30
-8n + n2 = 0 + 30

Combine like terms: 0 + 30 = 30
-8n + n2 = 30

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 = 30 + 16

Reorder the terms:
16 + -8n + n2 = 30 + 16

Combine like terms: 30 + 16 = 46
16 + -8n + n2 = 46

Factor a perfect square on the left side:
(n + -4)(n + -4) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(n + -4) equal to 6.782329983 and -6.782329983.


Subproblem 1
n + -4 = 6.782329983

Simplifying
n + -4 = 6.782329983

Reorder the terms:
-4 + n = 6.782329983

Solving
-4 + n = 6.782329983

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 = 6.782329983 + 4

Combine like terms: -4 + 4 = 0
0 + n = 6.782329983 + 4
n = 6.782329983 + 4

Combine like terms: 6.782329983 + 4 = 10.782329983
n = 10.782329983

Simplifying
n = 10.782329983


Subproblem 2
n + -4 = -6.782329983

Simplifying
n + -4 = -6.782329983

Reorder the terms:
-4 + n = -6.782329983

Solving
-4 + n = -6.782329983

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 = -6.782329983 + 4

Combine like terms: -4 + 4 = 0
0 + n = -6.782329983 + 4
n = -6.782329983 + 4

Combine like terms: -6.782329983 + 4 = -2.782329983
n = -2.782329983

Simplifying
n = -2.782329983


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {10.782329983, -2.782329983}

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