n^2-3n-99=0

Solution for n^2-3n-99=0 equation:

Simplifying
n2 + -3n + -99 = 0

Reorder the terms:
-99 + -3n + n2 = 0

Solving
-99 + -3n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '99' to each side of the equation.
-99 + -3n + 99 + n2 = 0 + 99

Reorder the terms:
-99 + 99 + -3n + n2 = 0 + 99

Combine like terms: -99 + 99 = 0
0 + -3n + n2 = 0 + 99
-3n + n2 = 0 + 99

Combine like terms: 0 + 99 = 99
-3n + n2 = 99

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = 99 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 99 + 2.25

Combine like terms: 99 + 2.25 = 101.25
2.25 + -3n + n2 = 101.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 101.25

Calculate the square root of the right side: 10.062305899

Break this problem into two subproblems by setting 
(n + -1.5) equal to 10.062305899 and -10.062305899.

Subproblem 1
n + -1.5 = 10.062305899

Simplifying
n + -1.5 = 10.062305899

Reorder the terms:
-1.5 + n = 10.062305899

Solving
-1.5 + n = 10.062305899

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = 10.062305899 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = 10.062305899 + 1.5
n = 10.062305899 + 1.5

Combine like terms: 10.062305899 + 1.5 = 11.562305899
n = 11.562305899

Simplifying
n = 11.562305899

Subproblem 2
n + -1.5 = -10.062305899

Simplifying
n + -1.5 = -10.062305899

Reorder the terms:
-1.5 + n = -10.062305899

Solving
-1.5 + n = -10.062305899

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = -10.062305899 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = -10.062305899 + 1.5
n = -10.062305899 + 1.5

Combine like terms: -10.062305899 + 1.5 = -8.562305899
n = -8.562305899

Simplifying
n = -8.562305899

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {11.562305899, -8.562305899}