n^2+14n-97=0

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Solution for n^2+14n-97=0 equation: 


Simplifying
n2 + 14n + -97 = 0

Reorder the terms:
-97 + 14n + n2 = 0

Solving
-97 + 14n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '97' to each side of the equation.
-97 + 14n + 97 + n2 = 0 + 97

Reorder the terms:
-97 + 97 + 14n + n2 = 0 + 97

Combine like terms: -97 + 97 = 0
0 + 14n + n2 = 0 + 97
14n + n2 = 0 + 97

Combine like terms: 0 + 97 = 97
14n + n2 = 97

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 = 97 + 49

Reorder the terms:
49 + 14n + n2 = 97 + 49

Combine like terms: 97 + 49 = 146
49 + 14n + n2 = 146

Factor a perfect square on the left side:
(n + 7)(n + 7) = 146

Calculate the square root of the right side: 12.083045974

Break this problem into two subproblems by setting 
(n + 7) equal to 12.083045974 and -12.083045974.


Subproblem 1
n + 7 = 12.083045974

Simplifying
n + 7 = 12.083045974

Reorder the terms:
7 + n = 12.083045974

Solving
7 + n = 12.083045974

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 = 12.083045974 + -7

Combine like terms: 7 + -7 = 0
0 + n = 12.083045974 + -7
n = 12.083045974 + -7

Combine like terms: 12.083045974 + -7 = 5.083045974
n = 5.083045974

Simplifying
n = 5.083045974


Subproblem 2
n + 7 = -12.083045974

Simplifying
n + 7 = -12.083045974

Reorder the terms:
7 + n = -12.083045974

Solving
7 + n = -12.083045974

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 = -12.083045974 + -7

Combine like terms: 7 + -7 = 0
0 + n = -12.083045974 + -7
n = -12.083045974 + -7

Combine like terms: -12.083045974 + -7 = -19.083045974
n = -19.083045974

Simplifying
n = -19.083045974


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {5.083045974, -19.083045974}

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