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

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

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

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

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

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

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

Solving
-2k = 3 + -1k + -1k2

Solving for variable 'k'.

Reorder the terms:
-3 + -2k + k + k2 = 3 + -1k + -1k2 + -3 + k + k2

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

Reorder the terms:
-3 + -1k + k2 = 3 + -3 + -1k + k + -1k2 + k2

Combine like terms: 3 + -3 = 0
-3 + -1k + k2 = 0 + -1k + k + -1k2 + k2
-3 + -1k + k2 = -1k + k + -1k2 + k2

Combine like terms: -1k + k = 0
-3 + -1k + k2 = 0 + -1k2 + k2
-3 + -1k + k2 = -1k2 + k2

Combine like terms: -1k2 + k2 = 0
-3 + -1k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -1k + 3 + k2 = 0 + 3

Reorder the terms:
-3 + 3 + -1k + k2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1k + k2 = 0 + 3
-1k + k2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1k + k2 = 3

The k term is -1k.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1k + 0.25 + k2 = 3 + 0.25

Reorder the terms:
0.25 + -1k + k2 = 3 + 0.25

Combine like terms: 3 + 0.25 = 3.25
0.25 + -1k + k2 = 3.25

Factor a perfect square on the left side:
(k + -0.5)(k + -0.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(k + -0.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
k + -0.5 = 1.802775638

Simplifying
k + -0.5 = 1.802775638

Reorder the terms:
-0.5 + k = 1.802775638

Solving
-0.5 + k = 1.802775638

Solving for variable 'k'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + k = 1.802775638 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + k = 1.802775638 + 0.5
k = 1.802775638 + 0.5

Combine like terms: 1.802775638 + 0.5 = 2.302775638
k = 2.302775638

Simplifying
k = 2.302775638

Subproblem 2
k + -0.5 = -1.802775638

Simplifying
k + -0.5 = -1.802775638

Reorder the terms:
-0.5 + k = -1.802775638

Solving
-0.5 + k = -1.802775638

Solving for variable 'k'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + k = -1.802775638 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + k = -1.802775638 + 0.5
k = -1.802775638 + 0.5

Combine like terms: -1.802775638 + 0.5 = -1.302775638
k = -1.302775638

Simplifying
k = -1.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2.302775638, -1.302775638}