2w^4-18=0

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Solution for 2w^4-18=0 equation:


Simplifying
2w4 + -18 = 0

Reorder the terms:
-18 + 2w4 = 0

Solving
-18 + 2w4 = 0

Solving for variable 'w'.

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

Add '18' to each side of the equation.
-18 + 18 + 2w4 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 2w4 = 0 + 18
2w4 = 0 + 18

Combine like terms: 0 + 18 = 18
2w4 = 18

Divide each side by '2'.
w4 = 9

Simplifying
w4 = 9

Reorder the terms:
-9 + w4 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + w4 = 0

Factor a difference between two squares.
(3 + w2)(-3 + w2) = 0

Subproblem 1

Set the factor '(3 + w2)' equal to zero and attempt to solve: Simplifying 3 + w2 = 0 Solving 3 + w2 = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + w2 = 0 + -3 w2 = 0 + -3 Combine like terms: 0 + -3 = -3 w2 = -3 Simplifying w2 = -3 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 '(-3 + w2)' equal to zero and attempt to solve: Simplifying -3 + w2 = 0 Solving -3 + w2 = 0 Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + w2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + w2 = 0 + 3 w2 = 0 + 3 Combine like terms: 0 + 3 = 3 w2 = 3 Simplifying w2 = 3 Take the square root of each side: w = {-1.732050808, 1.732050808}

Solution

w = {-1.732050808, 1.732050808}

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