2w^4-9w^2+4=0

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

Simplifying
2w4 + -9w2 + 4 = 0

Reorder the terms:
4 + -9w2 + 2w4 = 0

Solving
4 + -9w2 + 2w4 = 0

Solving for variable 'w'.

Factor a trinomial.
(1 + -2w2)(4 + -1w2) = 0

Factor a difference between two squares.
(1 + -2w2)((2 + w)(2 + -1w)) = 0

Subproblem 1
Set the factor '(1 + -2w2)' equal to zero and attempt to solve:

Simplifying
1 + -2w2 = 0

Solving
1 + -2w2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2w2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2w2 = 0 + -1
-2w2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2w2 = -1

Divide each side by '-2'.
w2 = 0.5

Simplifying
w2 = 0.5

Take the square root of each side:
w = {-0.707106781, 0.707106781}
Subproblem 2
Set the factor '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 0

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

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

Combine like terms: 2 + -2 = 0
0 + w = 0 + -2
w = 0 + -2

Combine like terms: 0 + -2 = -2
w = -2

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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

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

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

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

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {-0.707106781, 0.707106781, -2, 2}