n^2-16n-24=-8

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Solution for n^2-16n-24=-8 equation: 


Simplifying
n2 + -16n + -24 = -8

Reorder the terms:
-24 + -16n + n2 = -8

Solving
-24 + -16n + n2 = -8

Solving for variable 'n'.

Reorder the terms:
-24 + 8 + -16n + n2 = -8 + 8

Combine like terms: -24 + 8 = -16
-16 + -16n + n2 = -8 + 8

Combine like terms: -8 + 8 = 0
-16 + -16n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -16n + 16 + n2 = 0 + 16

Reorder the terms:
-16 + 16 + -16n + n2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -16n + n2 = 0 + 16
-16n + n2 = 0 + 16

Combine like terms: 0 + 16 = 16
-16n + n2 = 16

The n term is -16n.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16n + 64 + n2 = 16 + 64

Reorder the terms:
64 + -16n + n2 = 16 + 64

Combine like terms: 16 + 64 = 80
64 + -16n + n2 = 80

Factor a perfect square on the left side:
(n + -8)(n + -8) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(n + -8) equal to 8.94427191 and -8.94427191.


Subproblem 1
n + -8 = 8.94427191

Simplifying
n + -8 = 8.94427191

Reorder the terms:
-8 + n = 8.94427191

Solving
-8 + n = 8.94427191

Solving for variable 'n'.

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

Add '8' to each side of the equation.
-8 + 8 + n = 8.94427191 + 8

Combine like terms: -8 + 8 = 0
0 + n = 8.94427191 + 8
n = 8.94427191 + 8

Combine like terms: 8.94427191 + 8 = 16.94427191
n = 16.94427191

Simplifying
n = 16.94427191


Subproblem 2
n + -8 = -8.94427191

Simplifying
n + -8 = -8.94427191

Reorder the terms:
-8 + n = -8.94427191

Solving
-8 + n = -8.94427191

Solving for variable 'n'.

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

Add '8' to each side of the equation.
-8 + 8 + n = -8.94427191 + 8

Combine like terms: -8 + 8 = 0
0 + n = -8.94427191 + 8
n = -8.94427191 + 8

Combine like terms: -8.94427191 + 8 = -0.94427191
n = -0.94427191

Simplifying
n = -0.94427191


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {16.94427191, -0.94427191}

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