n^2+2n-20=0

Solution for n^2+2n-20=0 equation:

Simplifying
n2 + 2n + -20 = 0

Reorder the terms:
-20 + 2n + n2 = 0

Solving
-20 + 2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 2n + 20 + n2 = 0 + 20

Reorder the terms:
-20 + 20 + 2n + n2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 2n + n2 = 0 + 20
2n + n2 = 0 + 20

Combine like terms: 0 + 20 = 20
2n + n2 = 20

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = 20 + 1

Reorder the terms:
1 + 2n + n2 = 20 + 1

Combine like terms: 20 + 1 = 21
1 + 2n + n2 = 21

Factor a perfect square on the left side:
(n + 1)(n + 1) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(n + 1) equal to 4.582575695 and -4.582575695.

Subproblem 1
n + 1 = 4.582575695

Simplifying
n + 1 = 4.582575695

Reorder the terms:
1 + n = 4.582575695

Solving
1 + n = 4.582575695

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = 4.582575695 + -1

Combine like terms: 1 + -1 = 0
0 + n = 4.582575695 + -1
n = 4.582575695 + -1

Combine like terms: 4.582575695 + -1 = 3.582575695
n = 3.582575695

Simplifying
n = 3.582575695

Subproblem 2
n + 1 = -4.582575695

Simplifying
n + 1 = -4.582575695

Reorder the terms:
1 + n = -4.582575695

Solving
1 + n = -4.582575695

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = -4.582575695 + -1

Combine like terms: 1 + -1 = 0
0 + n = -4.582575695 + -1
n = -4.582575695 + -1

Combine like terms: -4.582575695 + -1 = -5.582575695
n = -5.582575695

Simplifying
n = -5.582575695

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.582575695, -5.582575695}