8n^2+16n-94=4

Solution for 8n^2+16n-94=4 equation:

Simplifying
8n2 + 16n + -94 = 4

Reorder the terms:
-94 + 16n + 8n2 = 4

Solving
-94 + 16n + 8n2 = 4

Solving for variable 'n'.

Reorder the terms:
-94 + -4 + 16n + 8n2 = 4 + -4

Combine like terms: -94 + -4 = -98
-98 + 16n + 8n2 = 4 + -4

Combine like terms: 4 + -4 = 0
-98 + 16n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-49 + 8n + 4n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-49 + 8n + 4n2)' equal to zero and attempt to solve:

Simplifying
-49 + 8n + 4n2 = 0

Solving
-49 + 8n + 4n2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-12.25 + 2n + n2 = 0

Move the constant term to the right:

Add '12.25' to each side of the equation.
-12.25 + 2n + 12.25 + n2 = 0 + 12.25

Reorder the terms:
-12.25 + 12.25 + 2n + n2 = 0 + 12.25

Combine like terms: -12.25 + 12.25 = 0.00
0.00 + 2n + n2 = 0 + 12.25
2n + n2 = 0 + 12.25

Combine like terms: 0 + 12.25 = 12.25
2n + n2 = 12.25

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 = 12.25 + 1

Reorder the terms:
1 + 2n + n2 = 12.25 + 1

Combine like terms: 12.25 + 1 = 13.25
1 + 2n + n2 = 13.25

Factor a perfect square on the left side:
(n + 1)(n + 1) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(n + 1) equal to 3.640054945 and -3.640054945.

Subproblem 1
n + 1 = 3.640054945

Simplifying
n + 1 = 3.640054945

Reorder the terms:
1 + n = 3.640054945

Solving
1 + n = 3.640054945

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 = 3.640054945 + -1

Combine like terms: 1 + -1 = 0
0 + n = 3.640054945 + -1
n = 3.640054945 + -1

Combine like terms: 3.640054945 + -1 = 2.640054945
n = 2.640054945

Simplifying
n = 2.640054945

Subproblem 2
n + 1 = -3.640054945

Simplifying
n + 1 = -3.640054945

Reorder the terms:
1 + n = -3.640054945

Solving
1 + n = -3.640054945

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 = -3.640054945 + -1

Combine like terms: 1 + -1 = 0
0 + n = -3.640054945 + -1
n = -3.640054945 + -1

Combine like terms: -3.640054945 + -1 = -4.640054945
n = -4.640054945

Simplifying
n = -4.640054945

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.640054945, -4.640054945}
Solution
n = {2.640054945, -4.640054945}