n^2-4n-14=0

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Solution for n^2-4n-14=0 equation: 


Simplifying
n2 + -4n + -14 = 0

Reorder the terms:
-14 + -4n + n2 = 0

Solving
-14 + -4n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -4n + 14 + n2 = 0 + 14

Reorder the terms:
-14 + 14 + -4n + n2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -4n + n2 = 0 + 14
-4n + n2 = 0 + 14

Combine like terms: 0 + 14 = 14
-4n + n2 = 14

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 = 14 + 4

Reorder the terms:
4 + -4n + n2 = 14 + 4

Combine like terms: 14 + 4 = 18
4 + -4n + n2 = 18

Factor a perfect square on the left side:
(n + -2)(n + -2) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(n + -2) equal to 4.242640687 and -4.242640687.


Subproblem 1
n + -2 = 4.242640687

Simplifying
n + -2 = 4.242640687

Reorder the terms:
-2 + n = 4.242640687

Solving
-2 + n = 4.242640687

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 = 4.242640687 + 2

Combine like terms: -2 + 2 = 0
0 + n = 4.242640687 + 2
n = 4.242640687 + 2

Combine like terms: 4.242640687 + 2 = 6.242640687
n = 6.242640687

Simplifying
n = 6.242640687


Subproblem 2
n + -2 = -4.242640687

Simplifying
n + -2 = -4.242640687

Reorder the terms:
-2 + n = -4.242640687

Solving
-2 + n = -4.242640687

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 = -4.242640687 + 2

Combine like terms: -2 + 2 = 0
0 + n = -4.242640687 + 2
n = -4.242640687 + 2

Combine like terms: -4.242640687 + 2 = -2.242640687
n = -2.242640687

Simplifying
n = -2.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6.242640687, -2.242640687}

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