n^2+2n-42=0

Solution for n^2+2n-42=0 equation:

Simplifying
n2 + 2n + -42 = 0

Reorder the terms:
-42 + 2n + n2 = 0

Solving
-42 + 2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + 2n + 42 + n2 = 0 + 42

Reorder the terms:
-42 + 42 + 2n + n2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 2n + n2 = 0 + 42
2n + n2 = 0 + 42

Combine like terms: 0 + 42 = 42
2n + n2 = 42

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 = 42 + 1

Reorder the terms:
1 + 2n + n2 = 42 + 1

Combine like terms: 42 + 1 = 43
1 + 2n + n2 = 43

Factor a perfect square on the left side:
(n + 1)(n + 1) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(n + 1) equal to 6.557438524 and -6.557438524.

Subproblem 1
n + 1 = 6.557438524

Simplifying
n + 1 = 6.557438524

Reorder the terms:
1 + n = 6.557438524

Solving
1 + n = 6.557438524

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 = 6.557438524 + -1

Combine like terms: 1 + -1 = 0
0 + n = 6.557438524 + -1
n = 6.557438524 + -1

Combine like terms: 6.557438524 + -1 = 5.557438524
n = 5.557438524

Simplifying
n = 5.557438524

Subproblem 2
n + 1 = -6.557438524

Simplifying
n + 1 = -6.557438524

Reorder the terms:
1 + n = -6.557438524

Solving
1 + n = -6.557438524

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 = -6.557438524 + -1

Combine like terms: 1 + -1 = 0
0 + n = -6.557438524 + -1
n = -6.557438524 + -1

Combine like terms: -6.557438524 + -1 = -7.557438524
n = -7.557438524

Simplifying
n = -7.557438524

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {5.557438524, -7.557438524}