n^2-2n+1=6

Solution for n^2-2n+1=6 equation:

Simplifying
n2 + -2n + 1 = 6

Reorder the terms:
1 + -2n + n2 = 6

Solving
1 + -2n + n2 = 6

Solving for variable 'n'.

Reorder the terms:
1 + -6 + -2n + n2 = 6 + -6

Combine like terms: 1 + -6 = -5
-5 + -2n + n2 = 6 + -6

Combine like terms: 6 + -6 = 0
-5 + -2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -2n + 5 + n2 = 0 + 5

Reorder the terms:
-5 + 5 + -2n + n2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2n + n2 = 0 + 5
-2n + n2 = 0 + 5

Combine like terms: 0 + 5 = 5
-2n + n2 = 5

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 = 5 + 1

Reorder the terms:
1 + -2n + n2 = 5 + 1

Combine like terms: 5 + 1 = 6
1 + -2n + n2 = 6

Factor a perfect square on the left side:
(n + -1)(n + -1) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(n + -1) equal to 2.449489743 and -2.449489743.

Subproblem 1
n + -1 = 2.449489743

Simplifying
n + -1 = 2.449489743

Reorder the terms:
-1 + n = 2.449489743

Solving
-1 + n = 2.449489743

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 = 2.449489743 + 1

Combine like terms: -1 + 1 = 0
0 + n = 2.449489743 + 1
n = 2.449489743 + 1

Combine like terms: 2.449489743 + 1 = 3.449489743
n = 3.449489743

Simplifying
n = 3.449489743

Subproblem 2
n + -1 = -2.449489743

Simplifying
n + -1 = -2.449489743

Reorder the terms:
-1 + n = -2.449489743

Solving
-1 + n = -2.449489743

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 = -2.449489743 + 1

Combine like terms: -1 + 1 = 0
0 + n = -2.449489743 + 1
n = -2.449489743 + 1

Combine like terms: -2.449489743 + 1 = -1.449489743
n = -1.449489743

Simplifying
n = -1.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.449489743, -1.449489743}