n^2+14n+20=0

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Solution for n^2+14n+20=0 equation: 


Simplifying
n2 + 14n + 20 = 0

Reorder the terms:
20 + 14n + n2 = 0

Solving
20 + 14n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + 14n + -20 + n2 = 0 + -20

Reorder the terms:
20 + -20 + 14n + n2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 14n + n2 = 0 + -20
14n + n2 = 0 + -20

Combine like terms: 0 + -20 = -20
14n + n2 = -20

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 = -20 + 49

Reorder the terms:
49 + 14n + n2 = -20 + 49

Combine like terms: -20 + 49 = 29
49 + 14n + n2 = 29

Factor a perfect square on the left side:
(n + 7)(n + 7) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(n + 7) equal to 5.385164807 and -5.385164807.


Subproblem 1
n + 7 = 5.385164807

Simplifying
n + 7 = 5.385164807

Reorder the terms:
7 + n = 5.385164807

Solving
7 + n = 5.385164807

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 = 5.385164807 + -7

Combine like terms: 7 + -7 = 0
0 + n = 5.385164807 + -7
n = 5.385164807 + -7

Combine like terms: 5.385164807 + -7 = -1.614835193
n = -1.614835193

Simplifying
n = -1.614835193


Subproblem 2
n + 7 = -5.385164807

Simplifying
n + 7 = -5.385164807

Reorder the terms:
7 + n = -5.385164807

Solving
7 + n = -5.385164807

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 = -5.385164807 + -7

Combine like terms: 7 + -7 = 0
0 + n = -5.385164807 + -7
n = -5.385164807 + -7

Combine like terms: -5.385164807 + -7 = -12.385164807
n = -12.385164807

Simplifying
n = -12.385164807


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-1.614835193, -12.385164807}

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