5w^4+50w^2-55=0

Solution for 5w^4+50w^2-55=0 equation:

Simplifying
5w4 + 50w2 + -55 = 0

Reorder the terms:
-55 + 50w2 + 5w4 = 0

Solving
-55 + 50w2 + 5w4 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-11 + 10w2 + w4) = 0

Factor a trinomial.
5((-11 + -1w2)(1 + -1w2)) = 0

Factor a difference between two squares.
5((-11 + -1w2)((1 + w)(1 + -1w))) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-11 + -1w2)' equal to zero and attempt to solve:

Simplifying
-11 + -1w2 = 0

Solving
-11 + -1w2 = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1w2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1w2 = 0 + 11
-1w2 = 0 + 11

Combine like terms: 0 + 11 = 11
-1w2 = 11

Divide each side by '-1'.
w2 = -11

Simplifying
w2 = -11

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 + 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 = {-1, 1}