n^2+2n-70=0

Solution for n^2+2n-70=0 equation:

Simplifying
n2 + 2n + -70 = 0

Reorder the terms:
-70 + 2n + n2 = 0

Solving
-70 + 2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + 2n + 70 + n2 = 0 + 70

Reorder the terms:
-70 + 70 + 2n + n2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 2n + n2 = 0 + 70
2n + n2 = 0 + 70

Combine like terms: 0 + 70 = 70
2n + n2 = 70

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 = 70 + 1

Reorder the terms:
1 + 2n + n2 = 70 + 1

Combine like terms: 70 + 1 = 71
1 + 2n + n2 = 71

Factor a perfect square on the left side:
(n + 1)(n + 1) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(n + 1) equal to 8.426149773 and -8.426149773.

Subproblem 1
n + 1 = 8.426149773

Simplifying
n + 1 = 8.426149773

Reorder the terms:
1 + n = 8.426149773

Solving
1 + n = 8.426149773

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 = 8.426149773 + -1

Combine like terms: 1 + -1 = 0
0 + n = 8.426149773 + -1
n = 8.426149773 + -1

Combine like terms: 8.426149773 + -1 = 7.426149773
n = 7.426149773

Simplifying
n = 7.426149773

Subproblem 2
n + 1 = -8.426149773

Simplifying
n + 1 = -8.426149773

Reorder the terms:
1 + n = -8.426149773

Solving
1 + n = -8.426149773

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 = -8.426149773 + -1

Combine like terms: 1 + -1 = 0
0 + n = -8.426149773 + -1
n = -8.426149773 + -1

Combine like terms: -8.426149773 + -1 = -9.426149773
n = -9.426149773

Simplifying
n = -9.426149773

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {7.426149773, -9.426149773}