(k-3)(k-1)=2

Solution for (k-3)(k-1)=2 equation:

Simplifying
(k + -3)(k + -1) = 2

Reorder the terms:
(-3 + k)(k + -1) = 2

Reorder the terms:
(-3 + k)(-1 + k) = 2

Multiply (-3 + k) * (-1 + k)
(-3(-1 + k) + k(-1 + k)) = 2
((-1 * -3 + k * -3) + k(-1 + k)) = 2
((3 + -3k) + k(-1 + k)) = 2
(3 + -3k + (-1 * k + k * k)) = 2
(3 + -3k + (-1k + k2)) = 2

Combine like terms: -3k + -1k = -4k
(3 + -4k + k2) = 2

Solving
3 + -4k + k2 = 2

Solving for variable 'k'.

Reorder the terms:
3 + -2 + -4k + k2 = 2 + -2

Combine like terms: 3 + -2 = 1
1 + -4k + k2 = 2 + -2

Combine like terms: 2 + -2 = 0
1 + -4k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -4k + -1 + k2 = 0 + -1

Reorder the terms:
1 + -1 + -4k + k2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4k + k2 = 0 + -1
-4k + k2 = 0 + -1

Combine like terms: 0 + -1 = -1
-4k + k2 = -1

The k term is -4k.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4k + 4 + k2 = -1 + 4

Reorder the terms:
4 + -4k + k2 = -1 + 4

Combine like terms: -1 + 4 = 3
4 + -4k + k2 = 3

Factor a perfect square on the left side:
(k + -2)(k + -2) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(k + -2) equal to 1.732050808 and -1.732050808.

Subproblem 1
k + -2 = 1.732050808

Simplifying
k + -2 = 1.732050808

Reorder the terms:
-2 + k = 1.732050808

Solving
-2 + k = 1.732050808

Solving for variable 'k'.

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

Add '2' to each side of the equation.
-2 + 2 + k = 1.732050808 + 2

Combine like terms: -2 + 2 = 0
0 + k = 1.732050808 + 2
k = 1.732050808 + 2

Combine like terms: 1.732050808 + 2 = 3.732050808
k = 3.732050808

Simplifying
k = 3.732050808

Subproblem 2
k + -2 = -1.732050808

Simplifying
k + -2 = -1.732050808

Reorder the terms:
-2 + k = -1.732050808

Solving
-2 + k = -1.732050808

Solving for variable 'k'.

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

Add '2' to each side of the equation.
-2 + 2 + k = -1.732050808 + 2

Combine like terms: -2 + 2 = 0
0 + k = -1.732050808 + 2
k = -1.732050808 + 2

Combine like terms: -1.732050808 + 2 = 0.267949192
k = 0.267949192

Simplifying
k = 0.267949192

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {3.732050808, 0.267949192}