n^2+14n+44=0

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Solution for n^2+14n+44=0 equation: 


Simplifying
n2 + 14n + 44 = 0

Reorder the terms:
44 + 14n + n2 = 0

Solving
44 + 14n + 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 + 14n + -44 + n2 = 0 + -44

Reorder the terms:
44 + -44 + 14n + n2 = 0 + -44

Combine like terms: 44 + -44 = 0
0 + 14n + n2 = 0 + -44
14n + n2 = 0 + -44

Combine like terms: 0 + -44 = -44
14n + n2 = -44

The n term is 14n.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14n + 49 + n2 = -44 + 49

Reorder the terms:
49 + 14n + n2 = -44 + 49

Combine like terms: -44 + 49 = 5
49 + 14n + n2 = 5

Factor a perfect square on the left side:
(n + 7)(n + 7) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(n + 7) equal to 2.236067978 and -2.236067978.


Subproblem 1
n + 7 = 2.236067978

Simplifying
n + 7 = 2.236067978

Reorder the terms:
7 + n = 2.236067978

Solving
7 + n = 2.236067978

Solving for variable 'n'.

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

Add '-7' to each side of the equation.
7 + -7 + n = 2.236067978 + -7

Combine like terms: 7 + -7 = 0
0 + n = 2.236067978 + -7
n = 2.236067978 + -7

Combine like terms: 2.236067978 + -7 = -4.763932022
n = -4.763932022

Simplifying
n = -4.763932022


Subproblem 2
n + 7 = -2.236067978

Simplifying
n + 7 = -2.236067978

Reorder the terms:
7 + n = -2.236067978

Solving
7 + n = -2.236067978

Solving for variable 'n'.

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

Add '-7' to each side of the equation.
7 + -7 + n = -2.236067978 + -7

Combine like terms: 7 + -7 = 0
0 + n = -2.236067978 + -7
n = -2.236067978 + -7

Combine like terms: -2.236067978 + -7 = -9.236067978
n = -9.236067978

Simplifying
n = -9.236067978


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-4.763932022, -9.236067978}

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