n^2-2n-10=0

Solution for n^2-2n-10=0 equation:

Simplifying
n2 + -2n + -10 = 0

Reorder the terms:
-10 + -2n + n2 = 0

Solving
-10 + -2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -2n + 10 + n2 = 0 + 10

Reorder the terms:
-10 + 10 + -2n + n2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -2n + n2 = 0 + 10
-2n + n2 = 0 + 10

Combine like terms: 0 + 10 = 10
-2n + n2 = 10

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 = 10 + 1

Reorder the terms:
1 + -2n + n2 = 10 + 1

Combine like terms: 10 + 1 = 11
1 + -2n + n2 = 11

Factor a perfect square on the left side:
(n + -1)(n + -1) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(n + -1) equal to 3.31662479 and -3.31662479.

Subproblem 1
n + -1 = 3.31662479

Simplifying
n + -1 = 3.31662479

Reorder the terms:
-1 + n = 3.31662479

Solving
-1 + n = 3.31662479

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 = 3.31662479 + 1

Combine like terms: -1 + 1 = 0
0 + n = 3.31662479 + 1
n = 3.31662479 + 1

Combine like terms: 3.31662479 + 1 = 4.31662479
n = 4.31662479

Simplifying
n = 4.31662479

Subproblem 2
n + -1 = -3.31662479

Simplifying
n + -1 = -3.31662479

Reorder the terms:
-1 + n = -3.31662479

Solving
-1 + n = -3.31662479

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 = -3.31662479 + 1

Combine like terms: -1 + 1 = 0
0 + n = -3.31662479 + 1
n = -3.31662479 + 1

Combine like terms: -3.31662479 + 1 = -2.31662479
n = -2.31662479

Simplifying
n = -2.31662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.31662479, -2.31662479}