n^2+6n-98=0

Solution for n^2+6n-98=0 equation:

Simplifying
n2 + 6n + -98 = 0

Reorder the terms:
-98 + 6n + n2 = 0

Solving
-98 + 6n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '98' to each side of the equation.
-98 + 6n + 98 + n2 = 0 + 98

Reorder the terms:
-98 + 98 + 6n + n2 = 0 + 98

Combine like terms: -98 + 98 = 0
0 + 6n + n2 = 0 + 98
6n + n2 = 0 + 98

Combine like terms: 0 + 98 = 98
6n + n2 = 98

The n term is 6n.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6n + 9 + n2 = 98 + 9

Reorder the terms:
9 + 6n + n2 = 98 + 9

Combine like terms: 98 + 9 = 107
9 + 6n + n2 = 107

Factor a perfect square on the left side:
(n + 3)(n + 3) = 107

Calculate the square root of the right side: 10.344080433

Break this problem into two subproblems by setting 
(n + 3) equal to 10.344080433 and -10.344080433.

Subproblem 1
n + 3 = 10.344080433

Simplifying
n + 3 = 10.344080433

Reorder the terms:
3 + n = 10.344080433

Solving
3 + n = 10.344080433

Solving for variable 'n'.

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

Add '-3' to each side of the equation.
3 + -3 + n = 10.344080433 + -3

Combine like terms: 3 + -3 = 0
0 + n = 10.344080433 + -3
n = 10.344080433 + -3

Combine like terms: 10.344080433 + -3 = 7.344080433
n = 7.344080433

Simplifying
n = 7.344080433

Subproblem 2
n + 3 = -10.344080433

Simplifying
n + 3 = -10.344080433

Reorder the terms:
3 + n = -10.344080433

Solving
3 + n = -10.344080433

Solving for variable 'n'.

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

Add '-3' to each side of the equation.
3 + -3 + n = -10.344080433 + -3

Combine like terms: 3 + -3 = 0
0 + n = -10.344080433 + -3
n = -10.344080433 + -3

Combine like terms: -10.344080433 + -3 = -13.344080433
n = -13.344080433

Simplifying
n = -13.344080433

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {7.344080433, -13.344080433}