n^2-14n-37=0

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Solution for n^2-14n-37=0 equation: 


Simplifying
n2 + -14n + -37 = 0

Reorder the terms:
-37 + -14n + n2 = 0

Solving
-37 + -14n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + -14n + 37 + n2 = 0 + 37

Reorder the terms:
-37 + 37 + -14n + n2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -14n + n2 = 0 + 37
-14n + n2 = 0 + 37

Combine like terms: 0 + 37 = 37
-14n + n2 = 37

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 = 37 + 49

Reorder the terms:
49 + -14n + n2 = 37 + 49

Combine like terms: 37 + 49 = 86
49 + -14n + n2 = 86

Factor a perfect square on the left side:
(n + -7)(n + -7) = 86

Calculate the square root of the right side: 9.273618495

Break this problem into two subproblems by setting 
(n + -7) equal to 9.273618495 and -9.273618495.


Subproblem 1
n + -7 = 9.273618495

Simplifying
n + -7 = 9.273618495

Reorder the terms:
-7 + n = 9.273618495

Solving
-7 + n = 9.273618495

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 = 9.273618495 + 7

Combine like terms: -7 + 7 = 0
0 + n = 9.273618495 + 7
n = 9.273618495 + 7

Combine like terms: 9.273618495 + 7 = 16.273618495
n = 16.273618495

Simplifying
n = 16.273618495


Subproblem 2
n + -7 = -9.273618495

Simplifying
n + -7 = -9.273618495

Reorder the terms:
-7 + n = -9.273618495

Solving
-7 + n = -9.273618495

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 = -9.273618495 + 7

Combine like terms: -7 + 7 = 0
0 + n = -9.273618495 + 7
n = -9.273618495 + 7

Combine like terms: -9.273618495 + 7 = -2.273618495
n = -2.273618495

Simplifying
n = -2.273618495


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {16.273618495, -2.273618495}

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