n^2+4n-44=0

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Solution for n^2+4n-44=0 equation: 


Simplifying
n2 + 4n + -44 = 0

Reorder the terms:
-44 + 4n + n2 = 0

Solving
-44 + 4n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + 4n + 44 + n2 = 0 + 44

Reorder the terms:
-44 + 44 + 4n + n2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + 4n + n2 = 0 + 44
4n + n2 = 0 + 44

Combine like terms: 0 + 44 = 44
4n + n2 = 44

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 = 44 + 4

Reorder the terms:
4 + 4n + n2 = 44 + 4

Combine like terms: 44 + 4 = 48
4 + 4n + n2 = 48

Factor a perfect square on the left side:
(n + 2)(n + 2) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(n + 2) equal to 6.92820323 and -6.92820323.


Subproblem 1
n + 2 = 6.92820323

Simplifying
n + 2 = 6.92820323

Reorder the terms:
2 + n = 6.92820323

Solving
2 + n = 6.92820323

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 = 6.92820323 + -2

Combine like terms: 2 + -2 = 0
0 + n = 6.92820323 + -2
n = 6.92820323 + -2

Combine like terms: 6.92820323 + -2 = 4.92820323
n = 4.92820323

Simplifying
n = 4.92820323


Subproblem 2
n + 2 = -6.92820323

Simplifying
n + 2 = -6.92820323

Reorder the terms:
2 + n = -6.92820323

Solving
2 + n = -6.92820323

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 = -6.92820323 + -2

Combine like terms: 2 + -2 = 0
0 + n = -6.92820323 + -2
n = -6.92820323 + -2

Combine like terms: -6.92820323 + -2 = -8.92820323
n = -8.92820323

Simplifying
n = -8.92820323


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.92820323, -8.92820323}

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