(-4k^4+14+3k^2)+(-3k^4-14k^4-8)=0

Solution for (-4k^4+14+3k^2)+(-3k^4-14k^4-8)=0 equation:

Simplifying
(-4k4 + 14 + 3k2) + (-3k4 + -14k4 + -8) = 0

Reorder the terms:
(14 + 3k2 + -4k4) + (-3k4 + -14k4 + -8) = 0

Remove parenthesis around (14 + 3k2 + -4k4)
14 + 3k2 + -4k4 + (-3k4 + -14k4 + -8) = 0

Reorder the terms:
14 + 3k2 + -4k4 + (-8 + -3k4 + -14k4) = 0

Combine like terms: -3k4 + -14k4 = -17k4
14 + 3k2 + -4k4 + (-8 + -17k4) = 0

Remove parenthesis around (-8 + -17k4)
14 + 3k2 + -4k4 + -8 + -17k4 = 0

Reorder the terms:
14 + -8 + 3k2 + -4k4 + -17k4 = 0

Combine like terms: 14 + -8 = 6
6 + 3k2 + -4k4 + -17k4 = 0

Combine like terms: -4k4 + -17k4 = -21k4
6 + 3k2 + -21k4 = 0

Solving
6 + 3k2 + -21k4 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + k2 + -7k4) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + k2 + -7k4)' equal to zero and attempt to solve:

Simplifying
2 + k2 + -7k4 = 0

Solving
2 + k2 + -7k4 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-0.2857142857 + -0.1428571429k2 + k4 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + -0.1428571429k2 + 0.2857142857 + k4 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + -0.1428571429k2 + k4 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + -0.1428571429k2 + k4 = 0 + 0.2857142857
-0.1428571429k2 + k4 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
-0.1428571429k2 + k4 = 0.2857142857

The k term is k2.  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.
-0.1428571429k2 + 0.25 + k4 = 0.2857142857 + 0.25

Reorder the terms:
0.25 + -0.1428571429k2 + k4 = 0.2857142857 + 0.25

Combine like terms: 0.2857142857 + 0.25 = 0.5357142857
0.25 + -0.1428571429k2 + k4 = 0.5357142857

Factor a perfect square on the left side:
(k2 + 0.5)(k2 + 0.5) = 0.5357142857

Calculate the square root of the right side: 0.731925055

Break this problem into two subproblems by setting 
(k2 + 0.5) equal to 0.731925055 and -0.731925055.

Subproblem 1
k2 + 0.5 = 0.731925055

Simplifying
k2 + 0.5 = 0.731925055

Reorder the terms:
0.5 + k2 = 0.731925055

Solving
0.5 + k2 = 0.731925055

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 + k2 = 0.731925055 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + k2 = 0.731925055 + -0.5
k2 = 0.731925055 + -0.5

Combine like terms: 0.731925055 + -0.5 = 0.231925055
k2 = 0.231925055

Simplifying
k2 = 0.231925055

Take the square root of each side:
k = {-0.481585979, 0.481585979}

Subproblem 2
k2 + 0.5 = -0.731925055

Simplifying
k2 + 0.5 = -0.731925055

Reorder the terms:
0.5 + k2 = -0.731925055

Solving
0.5 + k2 = -0.731925055

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 + k2 = -0.731925055 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + k2 = -0.731925055 + -0.5
k2 = -0.731925055 + -0.5

Combine like terms: -0.731925055 + -0.5 = -1.231925055
k2 = -1.231925055

Simplifying
k2 = -1.231925055

Reorder the terms:
1.231925055 + k2 = -1.231925055 + 1.231925055

Combine like terms: -1.231925055 + 1.231925055 = 0.000000000
1.231925055 + k2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.