n^2+2n-49=0

Solution for n^2+2n-49=0 equation:

Simplifying
n2 + 2n + -49 = 0

Reorder the terms:
-49 + 2n + n2 = 0

Solving
-49 + 2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + 2n + 49 + n2 = 0 + 49

Reorder the terms:
-49 + 49 + 2n + n2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + 2n + n2 = 0 + 49
2n + n2 = 0 + 49

Combine like terms: 0 + 49 = 49
2n + n2 = 49

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 = 49 + 1

Reorder the terms:
1 + 2n + n2 = 49 + 1

Combine like terms: 49 + 1 = 50
1 + 2n + n2 = 50

Factor a perfect square on the left side:
(n + 1)(n + 1) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(n + 1) equal to 7.071067812 and -7.071067812.

Subproblem 1
n + 1 = 7.071067812

Simplifying
n + 1 = 7.071067812

Reorder the terms:
1 + n = 7.071067812

Solving
1 + n = 7.071067812

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 = 7.071067812 + -1

Combine like terms: 1 + -1 = 0
0 + n = 7.071067812 + -1
n = 7.071067812 + -1

Combine like terms: 7.071067812 + -1 = 6.071067812
n = 6.071067812

Simplifying
n = 6.071067812

Subproblem 2
n + 1 = -7.071067812

Simplifying
n + 1 = -7.071067812

Reorder the terms:
1 + n = -7.071067812

Solving
1 + n = -7.071067812

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 = -7.071067812 + -1

Combine like terms: 1 + -1 = 0
0 + n = -7.071067812 + -1
n = -7.071067812 + -1

Combine like terms: -7.071067812 + -1 = -8.071067812
n = -8.071067812

Simplifying
n = -8.071067812

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6.071067812, -8.071067812}