w^4-9w^2+8=0

Solution for w^4-9w^2+8=0 equation:

Simplifying
w4 + -9w2 + 8 = 0

Reorder the terms:
8 + -9w2 + w4 = 0

Solving
8 + -9w2 + w4 = 0

Solving for variable 'w'.

Factor a trinomial.
(1 + -1w2)(8 + -1w2) = 0

Factor a difference between two squares.
((1 + w)(1 + -1w))(8 + -1w2) = 0

Subproblem 1
Set the factor '(8 + -1w2)' equal to zero and attempt to solve:

Simplifying
8 + -1w2 = 0

Solving
8 + -1w2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1w2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1w2 = 0 + -8
-1w2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1w2 = -8

Divide each side by '-1'.
w2 = 8

Simplifying
w2 = 8

Take the square root of each side:
w = {-2.828427125, 2.828427125}
Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve:

Simplifying
1 + w = 0

Solving
1 + w = 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 + w = 0 + -1

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

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

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

Simplifying
1 + -1w = 0

Solving
1 + -1w = 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 + -1w = 0 + -1

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

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

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

Simplifying
w = 1
Solution
w = {-2.828427125, 2.828427125, -1, 1}