8n^2-16n-34=-2

Solution for 8n^2-16n-34=-2 equation:

Simplifying
8n2 + -16n + -34 = -2

Reorder the terms:
-34 + -16n + 8n2 = -2

Solving
-34 + -16n + 8n2 = -2

Solving for variable 'n'.

Reorder the terms:
-34 + 2 + -16n + 8n2 = -2 + 2

Combine like terms: -34 + 2 = -32
-32 + -16n + 8n2 = -2 + 2

Combine like terms: -2 + 2 = 0
-32 + -16n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-4 + -2n + n2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-4 + -2n + n2)' equal to zero and attempt to solve:

Simplifying
-4 + -2n + n2 = 0

Solving
-4 + -2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2n + 4 + n2 = 0 + 4

Reorder the terms:
-4 + 4 + -2n + n2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2n + n2 = 0 + 4
-2n + n2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2n + n2 = 4

The n term is -2n.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2n + 1 + n2 = 4 + 1

Reorder the terms:
1 + -2n + n2 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + -2n + n2 = 5

Factor a perfect square on the left side:
(n + -1)(n + -1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(n + -1) equal to 2.236067978 and -2.236067978.

Subproblem 1
n + -1 = 2.236067978

Simplifying
n + -1 = 2.236067978

Reorder the terms:
-1 + n = 2.236067978

Solving
-1 + n = 2.236067978

Solving for variable 'n'.

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

Add '1' to each side of the equation.
-1 + 1 + n = 2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + n = 2.236067978 + 1
n = 2.236067978 + 1

Combine like terms: 2.236067978 + 1 = 3.236067978
n = 3.236067978

Simplifying
n = 3.236067978

Subproblem 2
n + -1 = -2.236067978

Simplifying
n + -1 = -2.236067978

Reorder the terms:
-1 + n = -2.236067978

Solving
-1 + n = -2.236067978

Solving for variable 'n'.

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

Add '1' to each side of the equation.
-1 + 1 + n = -2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + n = -2.236067978 + 1
n = -2.236067978 + 1

Combine like terms: -2.236067978 + 1 = -1.236067978
n = -1.236067978

Simplifying
n = -1.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.236067978, -1.236067978}
Solution
n = {3.236067978, -1.236067978}