w^4-24w^2-25=0

Solution for w^4-24w^2-25=0 equation:

Simplifying
w4 + -24w2 + -25 = 0

Reorder the terms:
-25 + -24w2 + w4 = 0

Solving
-25 + -24w2 + w4 = 0

Solving for variable 'w'.

Factor a trinomial.
(-1 + -1w2)(25 + -1w2) = 0

Factor a difference between two squares.
(-1 + -1w2)((5 + w)(5 + -1w)) = 0

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

Simplifying
-1 + -1w2 = 0

Solving
-1 + -1w2 = 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 + -1w2 = 0 + 1

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

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

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

Simplifying
w2 = -1

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 '(5 + w)' equal to zero and attempt to solve:

Simplifying
5 + w = 0

Solving
5 + w = 0

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

Add '-5' to each side of the equation.
5 + -5 + w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + w = 0 + -5
w = 0 + -5

Combine like terms: 0 + -5 = -5
w = -5

Simplifying
w = -5
Subproblem 3
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {-5, 5}