n^2+4n-59=0

Solution for n^2+4n-59=0 equation:

Simplifying
n2 + 4n + -59 = 0

Reorder the terms:
-59 + 4n + n2 = 0

Solving
-59 + 4n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '59' to each side of the equation.
-59 + 4n + 59 + n2 = 0 + 59

Reorder the terms:
-59 + 59 + 4n + n2 = 0 + 59

Combine like terms: -59 + 59 = 0
0 + 4n + n2 = 0 + 59
4n + n2 = 0 + 59

Combine like terms: 0 + 59 = 59
4n + n2 = 59

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 = 59 + 4

Reorder the terms:
4 + 4n + n2 = 59 + 4

Combine like terms: 59 + 4 = 63
4 + 4n + n2 = 63

Factor a perfect square on the left side:
(n + 2)(n + 2) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(n + 2) equal to 7.937253933 and -7.937253933.

Subproblem 1
n + 2 = 7.937253933

Simplifying
n + 2 = 7.937253933

Reorder the terms:
2 + n = 7.937253933

Solving
2 + n = 7.937253933

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 = 7.937253933 + -2

Combine like terms: 2 + -2 = 0
0 + n = 7.937253933 + -2
n = 7.937253933 + -2

Combine like terms: 7.937253933 + -2 = 5.937253933
n = 5.937253933

Simplifying
n = 5.937253933

Subproblem 2
n + 2 = -7.937253933

Simplifying
n + 2 = -7.937253933

Reorder the terms:
2 + n = -7.937253933

Solving
2 + n = -7.937253933

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 = -7.937253933 + -2

Combine like terms: 2 + -2 = 0
0 + n = -7.937253933 + -2
n = -7.937253933 + -2

Combine like terms: -7.937253933 + -2 = -9.937253933
n = -9.937253933

Simplifying
n = -9.937253933

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {5.937253933, -9.937253933}