N^2-4N=-2

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Solution for N^2-4N=-2 equation: 


Simplifying
N2 + -4N = -2

Reorder the terms:
-4N + N2 = -2

Solving
-4N + N2 = -2

Solving for variable 'N'.

Reorder the terms:
2 + -4N + N2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + -4N + N2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -4N + -2 + N2 = 0 + -2

Reorder the terms:
2 + -2 + -4N + N2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -4N + N2 = 0 + -2
-4N + N2 = 0 + -2

Combine like terms: 0 + -2 = -2
-4N + N2 = -2

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 = -2 + 4

Reorder the terms:
4 + -4N + N2 = -2 + 4

Combine like terms: -2 + 4 = 2
4 + -4N + N2 = 2

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

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(N + -2) equal to 1.414213562 and -1.414213562.


Subproblem 1
N + -2 = 1.414213562

Simplifying
N + -2 = 1.414213562

Reorder the terms:
-2 + N = 1.414213562

Solving
-2 + N = 1.414213562

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 = 1.414213562 + 2

Combine like terms: -2 + 2 = 0
0 + N = 1.414213562 + 2
N = 1.414213562 + 2

Combine like terms: 1.414213562 + 2 = 3.414213562
N = 3.414213562

Simplifying
N = 3.414213562


Subproblem 2
N + -2 = -1.414213562

Simplifying
N + -2 = -1.414213562

Reorder the terms:
-2 + N = -1.414213562

Solving
-2 + N = -1.414213562

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 = -1.414213562 + 2

Combine like terms: -2 + 2 = 0
0 + N = -1.414213562 + 2
N = -1.414213562 + 2

Combine like terms: -1.414213562 + 2 = 0.585786438
N = 0.585786438

Simplifying
N = 0.585786438


Solution
The solution to the problem is based on the solutions
from the subproblems.
N = {3.414213562, 0.585786438}

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