n^2+n-480=0

Solution for n^2+n-480=0 equation:

Simplifying
n2 + n + -480 = 0

Reorder the terms:
-480 + n + n2 = 0

Solving
-480 + n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '480' to each side of the equation.
-480 + n + 480 + n2 = 0 + 480

Reorder the terms:
-480 + 480 + n + n2 = 0 + 480

Combine like terms: -480 + 480 = 0
0 + n + n2 = 0 + 480
n + n2 = 0 + 480

Combine like terms: 0 + 480 = 480
n + n2 = 480

The n term is n.  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.
n + 0.25 + n2 = 480 + 0.25

Reorder the terms:
0.25 + n + n2 = 480 + 0.25

Combine like terms: 480 + 0.25 = 480.25
0.25 + n + n2 = 480.25

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 480.25

Calculate the square root of the right side: 21.914607001

Break this problem into two subproblems by setting 
(n + 0.5) equal to 21.914607001 and -21.914607001.

Subproblem 1
n + 0.5 = 21.914607001

Simplifying
n + 0.5 = 21.914607001

Reorder the terms:
0.5 + n = 21.914607001

Solving
0.5 + n = 21.914607001

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 = 21.914607001 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 21.914607001 + -0.5
n = 21.914607001 + -0.5

Combine like terms: 21.914607001 + -0.5 = 21.414607001
n = 21.414607001

Simplifying
n = 21.414607001

Subproblem 2
n + 0.5 = -21.914607001

Simplifying
n + 0.5 = -21.914607001

Reorder the terms:
0.5 + n = -21.914607001

Solving
0.5 + n = -21.914607001

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 = -21.914607001 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -21.914607001 + -0.5
n = -21.914607001 + -0.5

Combine like terms: -21.914607001 + -0.5 = -22.414607001
n = -22.414607001

Simplifying
n = -22.414607001

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {21.414607001, -22.414607001}