n^2+4n-4=0

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


Simplifying
n2 + 4n + -4 = 0

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

Solving
-4 + 4n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 4 + 4

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

Combine like terms: 4 + 4 = 8
4 + 4n + n2 = 8

Factor a perfect square on the left side:
(n + 2)(n + 2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(n + 2) equal to 2.828427125 and -2.828427125.


Subproblem 1
n + 2 = 2.828427125

Simplifying
n + 2 = 2.828427125

Reorder the terms:
2 + n = 2.828427125

Solving
2 + n = 2.828427125

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 = 2.828427125 + -2

Combine like terms: 2 + -2 = 0
0 + n = 2.828427125 + -2
n = 2.828427125 + -2

Combine like terms: 2.828427125 + -2 = 0.828427125
n = 0.828427125

Simplifying
n = 0.828427125


Subproblem 2
n + 2 = -2.828427125

Simplifying
n + 2 = -2.828427125

Reorder the terms:
2 + n = -2.828427125

Solving
2 + n = -2.828427125

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 = -2.828427125 + -2

Combine like terms: 2 + -2 = 0
0 + n = -2.828427125 + -2
n = -2.828427125 + -2

Combine like terms: -2.828427125 + -2 = -4.828427125
n = -4.828427125

Simplifying
n = -4.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.828427125, -4.828427125}

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