n^2-14n-75=0

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Solution for n^2-14n-75=0 equation: 


Simplifying
n2 + -14n + -75 = 0

Reorder the terms:
-75 + -14n + n2 = 0

Solving
-75 + -14n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + -14n + 75 + n2 = 0 + 75

Reorder the terms:
-75 + 75 + -14n + n2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + -14n + n2 = 0 + 75
-14n + n2 = 0 + 75

Combine like terms: 0 + 75 = 75
-14n + n2 = 75

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 = 75 + 49

Reorder the terms:
49 + -14n + n2 = 75 + 49

Combine like terms: 75 + 49 = 124
49 + -14n + n2 = 124

Factor a perfect square on the left side:
(n + -7)(n + -7) = 124

Calculate the square root of the right side: 11.135528726

Break this problem into two subproblems by setting 
(n + -7) equal to 11.135528726 and -11.135528726.


Subproblem 1
n + -7 = 11.135528726

Simplifying
n + -7 = 11.135528726

Reorder the terms:
-7 + n = 11.135528726

Solving
-7 + n = 11.135528726

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 = 11.135528726 + 7

Combine like terms: -7 + 7 = 0
0 + n = 11.135528726 + 7
n = 11.135528726 + 7

Combine like terms: 11.135528726 + 7 = 18.135528726
n = 18.135528726

Simplifying
n = 18.135528726


Subproblem 2
n + -7 = -11.135528726

Simplifying
n + -7 = -11.135528726

Reorder the terms:
-7 + n = -11.135528726

Solving
-7 + n = -11.135528726

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 = -11.135528726 + 7

Combine like terms: -7 + 7 = 0
0 + n = -11.135528726 + 7
n = -11.135528726 + 7

Combine like terms: -11.135528726 + 7 = -4.135528726
n = -4.135528726

Simplifying
n = -4.135528726


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {18.135528726, -4.135528726}

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