4k^2-8k-3=3-5k^2

Solution for 4k^2-8k-3=3-5k^2 equation:

Simplifying
4k2 + -8k + -3 = 3 + -5k2

Reorder the terms:
-3 + -8k + 4k2 = 3 + -5k2

Solving
-3 + -8k + 4k2 = 3 + -5k2

Solving for variable 'k'.

Reorder the terms:
-3 + -3 + -8k + 4k2 + 5k2 = 3 + -5k2 + -3 + 5k2

Combine like terms: -3 + -3 = -6
-6 + -8k + 4k2 + 5k2 = 3 + -5k2 + -3 + 5k2

Combine like terms: 4k2 + 5k2 = 9k2
-6 + -8k + 9k2 = 3 + -5k2 + -3 + 5k2

Reorder the terms:
-6 + -8k + 9k2 = 3 + -3 + -5k2 + 5k2

Combine like terms: 3 + -3 = 0
-6 + -8k + 9k2 = 0 + -5k2 + 5k2
-6 + -8k + 9k2 = -5k2 + 5k2

Combine like terms: -5k2 + 5k2 = 0
-6 + -8k + 9k2 = 0

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

Divide each side by '9'.
-0.6666666667 + -0.8888888889k + k2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -0.8888888889k + 0.6666666667 + k2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -0.8888888889k + k2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -0.8888888889k + k2 = 0 + 0.6666666667
-0.8888888889k + k2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-0.8888888889k + k2 = 0.6666666667

The k term is -0.8888888889k.  Take half its coefficient (-0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
-0.8888888889k + 0.1975308642 + k2 = 0.6666666667 + 0.1975308642

Reorder the terms:
0.1975308642 + -0.8888888889k + k2 = 0.6666666667 + 0.1975308642

Combine like terms: 0.6666666667 + 0.1975308642 = 0.8641975309
0.1975308642 + -0.8888888889k + k2 = 0.8641975309

Factor a perfect square on the left side:
(k + -0.4444444445)(k + -0.4444444445) = 0.8641975309

Calculate the square root of the right side: 0.929622252

Break this problem into two subproblems by setting 
(k + -0.4444444445) equal to 0.929622252 and -0.929622252.

Subproblem 1
k + -0.4444444445 = 0.929622252

Simplifying
k + -0.4444444445 = 0.929622252

Reorder the terms:
-0.4444444445 + k = 0.929622252

Solving
-0.4444444445 + k = 0.929622252

Solving for variable 'k'.

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

Add '0.4444444445' to each side of the equation.
-0.4444444445 + 0.4444444445 + k = 0.929622252 + 0.4444444445

Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000
0.0000000000 + k = 0.929622252 + 0.4444444445
k = 0.929622252 + 0.4444444445

Combine like terms: 0.929622252 + 0.4444444445 = 1.3740666965
k = 1.3740666965

Simplifying
k = 1.3740666965

Subproblem 2
k + -0.4444444445 = -0.929622252

Simplifying
k + -0.4444444445 = -0.929622252

Reorder the terms:
-0.4444444445 + k = -0.929622252

Solving
-0.4444444445 + k = -0.929622252

Solving for variable 'k'.

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

Add '0.4444444445' to each side of the equation.
-0.4444444445 + 0.4444444445 + k = -0.929622252 + 0.4444444445

Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000
0.0000000000 + k = -0.929622252 + 0.4444444445
k = -0.929622252 + 0.4444444445

Combine like terms: -0.929622252 + 0.4444444445 = -0.4851778075
k = -0.4851778075

Simplifying
k = -0.4851778075

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.3740666965, -0.4851778075}