2n^2-8n-12=10

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Solution for 2n^2-8n-12=10 equation: 


Simplifying
2n2 + -8n + -12 = 10

Reorder the terms:
-12 + -8n + 2n2 = 10

Solving
-12 + -8n + 2n2 = 10

Solving for variable 'n'.

Reorder the terms:
-12 + -10 + -8n + 2n2 = 10 + -10

Combine like terms: -12 + -10 = -22
-22 + -8n + 2n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-22 + -8n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + -4n + n2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-11 + -4n + n2)' equal to zero and attempt to solve:

Simplifying
-11 + -4n + n2 = 0

Solving
-11 + -4n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -4n + 11 + n2 = 0 + 11

Reorder the terms:
-11 + 11 + -4n + n2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -4n + n2 = 0 + 11
-4n + n2 = 0 + 11

Combine like terms: 0 + 11 = 11
-4n + n2 = 11

The n term is -4n.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4n + 4 + n2 = 11 + 4

Reorder the terms:
4 + -4n + n2 = 11 + 4

Combine like terms: 11 + 4 = 15
4 + -4n + n2 = 15

Factor a perfect square on the left side:
(n + -2)(n + -2) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(n + -2) equal to 3.872983346 and -3.872983346.


Subproblem 1
n + -2 = 3.872983346

Simplifying
n + -2 = 3.872983346

Reorder the terms:
-2 + n = 3.872983346

Solving
-2 + n = 3.872983346

Solving for variable 'n'.

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

Add '2' to each side of the equation.
-2 + 2 + n = 3.872983346 + 2

Combine like terms: -2 + 2 = 0
0 + n = 3.872983346 + 2
n = 3.872983346 + 2

Combine like terms: 3.872983346 + 2 = 5.872983346
n = 5.872983346

Simplifying
n = 5.872983346


Subproblem 2
n + -2 = -3.872983346

Simplifying
n + -2 = -3.872983346

Reorder the terms:
-2 + n = -3.872983346

Solving
-2 + n = -3.872983346

Solving for variable 'n'.

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

Add '2' to each side of the equation.
-2 + 2 + n = -3.872983346 + 2

Combine like terms: -2 + 2 = 0
0 + n = -3.872983346 + 2
n = -3.872983346 + 2

Combine like terms: -3.872983346 + 2 = -1.872983346
n = -1.872983346

Simplifying
n = -1.872983346


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {5.872983346, -1.872983346}
Solution
n = {5.872983346, -1.872983346}

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