n*n-n-9=0

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Solution for n*n-n-9=0 equation: 


Simplifying
n * n + -1n + -9 = 0

Multiply n * n
n2 + -1n + -9 = 0

Reorder the terms:
-9 + -1n + n2 = 0

Solving
-9 + -1n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -1n + 9 + n2 = 0 + 9

Reorder the terms:
-9 + 9 + -1n + n2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1n + n2 = 0 + 9
-1n + n2 = 0 + 9

Combine like terms: 0 + 9 = 9
-1n + n2 = 9

The n term is -1n.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1n + 0.25 + n2 = 9 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 9 + 0.25

Combine like terms: 9 + 0.25 = 9.25
0.25 + -1n + n2 = 9.25

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(n + -0.5) equal to 3.041381265 and -3.041381265.


Subproblem 1
n + -0.5 = 3.041381265

Simplifying
n + -0.5 = 3.041381265

Reorder the terms:
-0.5 + n = 3.041381265

Solving
-0.5 + n = 3.041381265

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = 3.041381265 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = 3.041381265 + 0.5
n = 3.041381265 + 0.5

Combine like terms: 3.041381265 + 0.5 = 3.541381265
n = 3.541381265

Simplifying
n = 3.541381265


Subproblem 2
n + -0.5 = -3.041381265

Simplifying
n + -0.5 = -3.041381265

Reorder the terms:
-0.5 + n = -3.041381265

Solving
-0.5 + n = -3.041381265

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = -3.041381265 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = -3.041381265 + 0.5
n = -3.041381265 + 0.5

Combine like terms: -3.041381265 + 0.5 = -2.541381265
n = -2.541381265

Simplifying
n = -2.541381265


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.541381265, -2.541381265}

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