(n*n)+n=300

Solution for (n*n)+n=300 equation:

Simplifying
(n * n) + n = 300

Multiply n * n
(n2) + n = 300
n2 + n = 300

Reorder the terms:
n + n2 = 300

Solving
n + n2 = 300

Solving for variable 'n'.

Reorder the terms:
-300 + n + n2 = 300 + -300

Combine like terms: 300 + -300 = 0
-300 + n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + n + 300 + n2 = 0 + 300

Reorder the terms:
-300 + 300 + n + n2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + n + n2 = 0 + 300
n + n2 = 0 + 300

Combine like terms: 0 + 300 = 300
n + n2 = 300

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 = 300 + 0.25

Reorder the terms:
0.25 + n + n2 = 300 + 0.25

Combine like terms: 300 + 0.25 = 300.25
0.25 + n + n2 = 300.25

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 300.25

Calculate the square root of the right side: 17.327723451

Break this problem into two subproblems by setting 
(n + 0.5) equal to 17.327723451 and -17.327723451.

Subproblem 1
n + 0.5 = 17.327723451

Simplifying
n + 0.5 = 17.327723451

Reorder the terms:
0.5 + n = 17.327723451

Solving
0.5 + n = 17.327723451

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 = 17.327723451 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 17.327723451 + -0.5
n = 17.327723451 + -0.5

Combine like terms: 17.327723451 + -0.5 = 16.827723451
n = 16.827723451

Simplifying
n = 16.827723451

Subproblem 2
n + 0.5 = -17.327723451

Simplifying
n + 0.5 = -17.327723451

Reorder the terms:
0.5 + n = -17.327723451

Solving
0.5 + n = -17.327723451

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 = -17.327723451 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -17.327723451 + -0.5
n = -17.327723451 + -0.5

Combine like terms: -17.327723451 + -0.5 = -17.827723451
n = -17.827723451

Simplifying
n = -17.827723451

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {16.827723451, -17.827723451}