n^2-15n-36=0

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Solution for n^2-15n-36=0 equation: 


Simplifying
n2 + -15n + -36 = 0

Reorder the terms:
-36 + -15n + n2 = 0

Solving
-36 + -15n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -15n + 36 + n2 = 0 + 36

Reorder the terms:
-36 + 36 + -15n + n2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -15n + n2 = 0 + 36
-15n + n2 = 0 + 36

Combine like terms: 0 + 36 = 36
-15n + n2 = 36

The n term is -15n.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15n + 56.25 + n2 = 36 + 56.25

Reorder the terms:
56.25 + -15n + n2 = 36 + 56.25

Combine like terms: 36 + 56.25 = 92.25
56.25 + -15n + n2 = 92.25

Factor a perfect square on the left side:
(n + -7.5)(n + -7.5) = 92.25

Calculate the square root of the right side: 9.604686356

Break this problem into two subproblems by setting 
(n + -7.5) equal to 9.604686356 and -9.604686356.


Subproblem 1
n + -7.5 = 9.604686356

Simplifying
n + -7.5 = 9.604686356

Reorder the terms:
-7.5 + n = 9.604686356

Solving
-7.5 + n = 9.604686356

Solving for variable 'n'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + n = 9.604686356 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + n = 9.604686356 + 7.5
n = 9.604686356 + 7.5

Combine like terms: 9.604686356 + 7.5 = 17.104686356
n = 17.104686356

Simplifying
n = 17.104686356


Subproblem 2
n + -7.5 = -9.604686356

Simplifying
n + -7.5 = -9.604686356

Reorder the terms:
-7.5 + n = -9.604686356

Solving
-7.5 + n = -9.604686356

Solving for variable 'n'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + n = -9.604686356 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + n = -9.604686356 + 7.5
n = -9.604686356 + 7.5

Combine like terms: -9.604686356 + 7.5 = -2.104686356
n = -2.104686356

Simplifying
n = -2.104686356


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {17.104686356, -2.104686356}

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