n^2+7n+16=5

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Solution for n^2+7n+16=5 equation: 


Simplifying
n2 + 7n + 16 = 5

Reorder the terms:
16 + 7n + n2 = 5

Solving
16 + 7n + n2 = 5

Solving for variable 'n'.

Reorder the terms:
16 + -5 + 7n + n2 = 5 + -5

Combine like terms: 16 + -5 = 11
11 + 7n + n2 = 5 + -5

Combine like terms: 5 + -5 = 0
11 + 7n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 7n + -11 + n2 = 0 + -11

Reorder the terms:
11 + -11 + 7n + n2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 7n + n2 = 0 + -11
7n + n2 = 0 + -11

Combine like terms: 0 + -11 = -11
7n + n2 = -11

The n term is 7n.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7n + 12.25 + n2 = -11 + 12.25

Reorder the terms:
12.25 + 7n + n2 = -11 + 12.25

Combine like terms: -11 + 12.25 = 1.25
12.25 + 7n + n2 = 1.25

Factor a perfect square on the left side:
(n + 3.5)(n + 3.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(n + 3.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
n + 3.5 = 1.118033989

Simplifying
n + 3.5 = 1.118033989

Reorder the terms:
3.5 + n = 1.118033989

Solving
3.5 + n = 1.118033989

Solving for variable 'n'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + n = 1.118033989 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + n = 1.118033989 + -3.5
n = 1.118033989 + -3.5

Combine like terms: 1.118033989 + -3.5 = -2.381966011
n = -2.381966011

Simplifying
n = -2.381966011


Subproblem 2
n + 3.5 = -1.118033989

Simplifying
n + 3.5 = -1.118033989

Reorder the terms:
3.5 + n = -1.118033989

Solving
3.5 + n = -1.118033989

Solving for variable 'n'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + n = -1.118033989 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + n = -1.118033989 + -3.5
n = -1.118033989 + -3.5

Combine like terms: -1.118033989 + -3.5 = -4.618033989
n = -4.618033989

Simplifying
n = -4.618033989


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-2.381966011, -4.618033989}

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