3y^2-2yk-2k^2=

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Solution for 3y^2-2yk-2k^2= equation: 


Simplifying
3y2 + -2yk + -2k2 = 0

Reorder the terms:
-2ky + -2k2 + 3y2 = 0

Solving
-2ky + -2k2 + 3y2 = 0

Solving for variable 'k'.

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

Divide each side by '-2'.
ky + k2 + -1.5y2 = 0

Move the constant term to the right:

Add '1.5y2' to each side of the equation.
ky + k2 + -1.5y2 + 1.5y2 = 0 + 1.5y2

Combine like terms: -1.5y2 + 1.5y2 = 0.0
ky + k2 + 0.0 = 0 + 1.5y2
ky + k2 = 0 + 1.5y2
Remove the zero:
ky + k2 = 1.5y2

The k term is ky.  Take half its coefficient (0.5y).
Square it (0.25y2) and add it to both sides.

Add '0.25y2' to each side of the equation.
y2 + k2 + 0.25y2 = 1.5y2 + 0.25y2

Reorder the terms:
k2 + y2 + 0.25y2 = 1.5y2 + 0.25y2

Combine like terms: y2 + 0.25y2 = 1.25y2
k2 + 1.25y2 = 1.5y2 + 0.25y2

Combine like terms: 1.5y2 + 0.25y2 = 1.75y2
k2 + 1.25y2 = 1.75y2

Factor a perfect square on the left side:
(k + 0.5y)(k + 0.5y) = 1.75y2

Calculate the square root of the right side: 1.322875656y

Break this problem into two subproblems by setting 
(k + 0.5y) equal to 1.322875656y and -1.322875656y.


Subproblem 1
k + 0.5y = 1.322875656y

Simplifying
k + 0.5y = 1.322875656y

Solving
k + 0.5y = 1.322875656y

Solving for variable 'k'.

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

Add '-0.5y' to each side of the equation.
k + 0.5y + -0.5y = 1.322875656y + -0.5y

Combine like terms: 0.5y + -0.5y = 0.0
k + 0.0 = 1.322875656y + -0.5y
k = 1.322875656y + -0.5y

Combine like terms: 1.322875656y + -0.5y = 0.822875656y
k = 0.822875656y

Simplifying
k = 0.822875656y


Subproblem 2
k + 0.5y = -1.322875656y

Simplifying
k + 0.5y = -1.322875656y

Solving
k + 0.5y = -1.322875656y

Solving for variable 'k'.

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

Add '-0.5y' to each side of the equation.
k + 0.5y + -0.5y = -1.322875656y + -0.5y

Combine like terms: 0.5y + -0.5y = 0.0
k + 0.0 = -1.322875656y + -0.5y
k = -1.322875656y + -0.5y

Combine like terms: -1.322875656y + -0.5y = -1.822875656y
k = -1.822875656y

Simplifying
k = -1.822875656y


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.822875656y, -1.822875656y}

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