2n^2-2n-8=-2

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

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

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

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

Solving for variable 'n'.

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

Combine like terms: -8 + 2 = -6
-6 + -2n + 2n2 = -2 + 2

Combine like terms: -2 + 2 = 0
-6 + -2n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -1n + n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -1n + n2)' equal to zero and attempt to solve:

Simplifying
-3 + -1n + n2 = 0

Solving
-3 + -1n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -1n + 3 + n2 = 0 + 3

Reorder the terms:
-3 + 3 + -1n + n2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n + n2 = 0 + 3
-1n + n2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1n + n2 = 3

The n term is -1n.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1n + 0.25 + n2 = 3 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 3 + 0.25

Combine like terms: 3 + 0.25 = 3.25
0.25 + -1n + n2 = 3.25

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(n + -0.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
n + -0.5 = 1.802775638

Simplifying
n + -0.5 = 1.802775638

Reorder the terms:
-0.5 + n = 1.802775638

Solving
-0.5 + n = 1.802775638

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = 1.802775638 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = 1.802775638 + 0.5
n = 1.802775638 + 0.5

Combine like terms: 1.802775638 + 0.5 = 2.302775638
n = 2.302775638

Simplifying
n = 2.302775638

Subproblem 2
n + -0.5 = -1.802775638

Simplifying
n + -0.5 = -1.802775638

Reorder the terms:
-0.5 + n = -1.802775638

Solving
-0.5 + n = -1.802775638

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = -1.802775638 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = -1.802775638 + 0.5
n = -1.802775638 + 0.5

Combine like terms: -1.802775638 + 0.5 = -1.302775638
n = -1.302775638

Simplifying
n = -1.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.302775638, -1.302775638}
Solution
n = {2.302775638, -1.302775638}