w^4+8w^2-20=

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Solution for w^4+8w^2-20= equation: 


Simplifying
w4 + 8w2 + -20 = 0

Reorder the terms:
-20 + 8w2 + w4 = 0

Solving
-20 + 8w2 + w4 = 0

Solving for variable 'w'.

Factor a trinomial.
(-10 + -1w2)(2 + -1w2) = 0


Subproblem 1
Set the factor '(-10 + -1w2)' equal to zero and attempt to solve:

Simplifying
-10 + -1w2 = 0

Solving
-10 + -1w2 = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1w2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1w2 = 0 + 10
-1w2 = 0 + 10

Combine like terms: 0 + 10 = 10
-1w2 = 10

Divide each side by '-1'.
w2 = -10

Simplifying
w2 = -10

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 '(2 + -1w2)' equal to zero and attempt to solve:

Simplifying
2 + -1w2 = 0

Solving
2 + -1w2 = 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 + -1w2 = 0 + -2

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

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

Divide each side by '-1'.
w2 = 2

Simplifying
w2 = 2

Take the square root of each side:
w = {-1.414213562, 1.414213562}
Solution
w = {-1.414213562, 1.414213562}

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