(k-2)(2k+2)=5

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Solution for (k-2)(2k+2)=5 equation: 


Simplifying
(k + -2)(2k + 2) = 5

Reorder the terms:
(-2 + k)(2k + 2) = 5

Reorder the terms:
(-2 + k)(2 + 2k) = 5

Multiply (-2 + k) * (2 + 2k)
(-2(2 + 2k) + k(2 + 2k)) = 5
((2 * -2 + 2k * -2) + k(2 + 2k)) = 5
((-4 + -4k) + k(2 + 2k)) = 5
(-4 + -4k + (2 * k + 2k * k)) = 5
(-4 + -4k + (2k + 2k2)) = 5

Combine like terms: -4k + 2k = -2k
(-4 + -2k + 2k2) = 5

Solving
-4 + -2k + 2k2 = 5

Solving for variable 'k'.

Reorder the terms:
-4 + -5 + -2k + 2k2 = 5 + -5

Combine like terms: -4 + -5 = -9
-9 + -2k + 2k2 = 5 + -5

Combine like terms: 5 + -5 = 0
-9 + -2k + 2k2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-4.5 + -1k + k2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -1k + 4.5 + k2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -1k + k2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -1k + k2 = 0 + 4.5
-1k + k2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-1k + k2 = 4.5

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 = 4.5 + 0.25

Reorder the terms:
0.25 + -1k + k2 = 4.5 + 0.25

Combine like terms: 4.5 + 0.25 = 4.75
0.25 + -1k + k2 = 4.75

Factor a perfect square on the left side:
(k + -0.5)(k + -0.5) = 4.75

Calculate the square root of the right side: 2.179449472

Break this problem into two subproblems by setting 
(k + -0.5) equal to 2.179449472 and -2.179449472.


Subproblem 1
k + -0.5 = 2.179449472

Simplifying
k + -0.5 = 2.179449472

Reorder the terms:
-0.5 + k = 2.179449472

Solving
-0.5 + k = 2.179449472

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 = 2.179449472 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + k = 2.179449472 + 0.5
k = 2.179449472 + 0.5

Combine like terms: 2.179449472 + 0.5 = 2.679449472
k = 2.679449472

Simplifying
k = 2.679449472


Subproblem 2
k + -0.5 = -2.179449472

Simplifying
k + -0.5 = -2.179449472

Reorder the terms:
-0.5 + k = -2.179449472

Solving
-0.5 + k = -2.179449472

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 = -2.179449472 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + k = -2.179449472 + 0.5
k = -2.179449472 + 0.5

Combine like terms: -2.179449472 + 0.5 = -1.679449472
k = -1.679449472

Simplifying
k = -1.679449472


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2.679449472, -1.679449472}

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