n^2-5n+6=1

Solution for n^2-5n+6=1 equation:

Simplifying
n2 + -5n + 6 = 1

Reorder the terms:
6 + -5n + n2 = 1

Solving
6 + -5n + n2 = 1

Solving for variable 'n'.

Reorder the terms:
6 + -1 + -5n + n2 = 1 + -1

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

Combine like terms: 1 + -1 = 0
5 + -5n + n2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The n term is -5n.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5n + 6.25 + n2 = -5 + 6.25

Reorder the terms:
6.25 + -5n + n2 = -5 + 6.25

Combine like terms: -5 + 6.25 = 1.25
6.25 + -5n + n2 = 1.25

Factor a perfect square on the left side:
(n + -2.5)(n + -2.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(n + -2.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
n + -2.5 = 1.118033989

Simplifying
n + -2.5 = 1.118033989

Reorder the terms:
-2.5 + n = 1.118033989

Solving
-2.5 + n = 1.118033989

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '2.5' to each side of the equation.
-2.5 + 2.5 + n = 1.118033989 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + n = 1.118033989 + 2.5
n = 1.118033989 + 2.5

Combine like terms: 1.118033989 + 2.5 = 3.618033989
n = 3.618033989

Simplifying
n = 3.618033989

Subproblem 2
n + -2.5 = -1.118033989

Simplifying
n + -2.5 = -1.118033989

Reorder the terms:
-2.5 + n = -1.118033989

Solving
-2.5 + n = -1.118033989

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '2.5' to each side of the equation.
-2.5 + 2.5 + n = -1.118033989 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + n = -1.118033989 + 2.5
n = -1.118033989 + 2.5

Combine like terms: -1.118033989 + 2.5 = 1.381966011
n = 1.381966011

Simplifying
n = 1.381966011

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.618033989, 1.381966011}