n^2+4n-30=0

Solution for n^2+4n-30=0 equation:

Simplifying
n2 + 4n + -30 = 0

Reorder the terms:
-30 + 4n + n2 = 0

Solving
-30 + 4n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 4n + 30 + n2 = 0 + 30

Reorder the terms:
-30 + 30 + 4n + n2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 4n + n2 = 0 + 30
4n + n2 = 0 + 30

Combine like terms: 0 + 30 = 30
4n + n2 = 30

The n term is 4n.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4n + 4 + n2 = 30 + 4

Reorder the terms:
4 + 4n + n2 = 30 + 4

Combine like terms: 30 + 4 = 34
4 + 4n + n2 = 34

Factor a perfect square on the left side:
(n + 2)(n + 2) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(n + 2) equal to 5.830951895 and -5.830951895.

Subproblem 1
n + 2 = 5.830951895

Simplifying
n + 2 = 5.830951895

Reorder the terms:
2 + n = 5.830951895

Solving
2 + n = 5.830951895

Solving for variable 'n'.

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

Add '-2' to each side of the equation.
2 + -2 + n = 5.830951895 + -2

Combine like terms: 2 + -2 = 0
0 + n = 5.830951895 + -2
n = 5.830951895 + -2

Combine like terms: 5.830951895 + -2 = 3.830951895
n = 3.830951895

Simplifying
n = 3.830951895

Subproblem 2
n + 2 = -5.830951895

Simplifying
n + 2 = -5.830951895

Reorder the terms:
2 + n = -5.830951895

Solving
2 + n = -5.830951895

Solving for variable 'n'.

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

Add '-2' to each side of the equation.
2 + -2 + n = -5.830951895 + -2

Combine like terms: 2 + -2 = 0
0 + n = -5.830951895 + -2
n = -5.830951895 + -2

Combine like terms: -5.830951895 + -2 = -7.830951895
n = -7.830951895

Simplifying
n = -7.830951895

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.830951895, -7.830951895}