N^2-13N-36=0

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Solution for N^2-13N-36=0 equation: 


Simplifying
N2 + -13N + -36 = 0

Reorder the terms:
-36 + -13N + N2 = 0

Solving
-36 + -13N + 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 + -13N + 36 + N2 = 0 + 36

Reorder the terms:
-36 + 36 + -13N + N2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -13N + N2 = 0 + 36
-13N + N2 = 0 + 36

Combine like terms: 0 + 36 = 36
-13N + N2 = 36

The N term is -13N.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13N + 42.25 + N2 = 36 + 42.25

Reorder the terms:
42.25 + -13N + N2 = 36 + 42.25

Combine like terms: 36 + 42.25 = 78.25
42.25 + -13N + N2 = 78.25

Factor a perfect square on the left side:
(N + -6.5)(N + -6.5) = 78.25

Calculate the square root of the right side: 8.845903006

Break this problem into two subproblems by setting 
(N + -6.5) equal to 8.845903006 and -8.845903006.


Subproblem 1
N + -6.5 = 8.845903006

Simplifying
N + -6.5 = 8.845903006

Reorder the terms:
-6.5 + N = 8.845903006

Solving
-6.5 + N = 8.845903006

Solving for variable 'N'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + N = 8.845903006 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + N = 8.845903006 + 6.5
N = 8.845903006 + 6.5

Combine like terms: 8.845903006 + 6.5 = 15.345903006
N = 15.345903006

Simplifying
N = 15.345903006


Subproblem 2
N + -6.5 = -8.845903006

Simplifying
N + -6.5 = -8.845903006

Reorder the terms:
-6.5 + N = -8.845903006

Solving
-6.5 + N = -8.845903006

Solving for variable 'N'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + N = -8.845903006 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + N = -8.845903006 + 6.5
N = -8.845903006 + 6.5

Combine like terms: -8.845903006 + 6.5 = -2.345903006
N = -2.345903006

Simplifying
N = -2.345903006


Solution
The solution to the problem is based on the solutions
from the subproblems.
N = {15.345903006, -2.345903006}

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