4k^4+35k^2-9=0

Solution for 4k^4+35k^2-9=0 equation:

Simplifying
4k4 + 35k2 + -9 = 0

Reorder the terms:
-9 + 35k2 + 4k4 = 0

Solving
-9 + 35k2 + 4k4 = 0

Solving for variable 'k'.

Factor a trinomial.
(-9 + -1k2)(1 + -4k2) = 0

Factor a difference between two squares.
(-9 + -1k2)((1 + 2k)(1 + -2k)) = 0

Subproblem 1
Set the factor '(-9 + -1k2)' equal to zero and attempt to solve:

Simplifying
-9 + -1k2 = 0

Solving
-9 + -1k2 = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1k2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1k2 = 0 + 9
-1k2 = 0 + 9

Combine like terms: 0 + 9 = 9
-1k2 = 9

Divide each side by '-1'.
k2 = -9

Simplifying
k2 = -9

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + 2k)' equal to zero and attempt to solve:

Simplifying
1 + 2k = 0

Solving
1 + 2k = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2k = 0 + -1
2k = 0 + -1

Combine like terms: 0 + -1 = -1
2k = -1

Divide each side by '2'.
k = -0.5

Simplifying
k = -0.5
Subproblem 3
Set the factor '(1 + -2k)' equal to zero and attempt to solve:

Simplifying
1 + -2k = 0

Solving
1 + -2k = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2k = 0 + -1
-2k = 0 + -1

Combine like terms: 0 + -1 = -1
-2k = -1

Divide each side by '-2'.
k = 0.5

Simplifying
k = 0.5
Solution
k = {-0.5, 0.5}