2w^4-162=0

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Solution for 2w^4-162=0 equation:


Simplifying
2w4 + -162 = 0

Reorder the terms:
-162 + 2w4 = 0

Solving
-162 + 2w4 = 0

Solving for variable 'w'.

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

Add '162' to each side of the equation.
-162 + 162 + 2w4 = 0 + 162

Combine like terms: -162 + 162 = 0
0 + 2w4 = 0 + 162
2w4 = 0 + 162

Combine like terms: 0 + 162 = 162
2w4 = 162

Divide each side by '2'.
w4 = 81

Simplifying
w4 = 81

Reorder the terms:
-81 + w4 = 81 + -81

Combine like terms: 81 + -81 = 0
-81 + w4 = 0

Factor a difference between two squares.
(9 + w2)(-9 + w2) = 0

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

Subproblem 1

Set the factor '(9 + w2)' equal to zero and attempt to solve: Simplifying 9 + w2 = 0 Solving 9 + w2 = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + w2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + w2 = 0 + -9 w2 = 0 + -9 Combine like terms: 0 + -9 = -9 w2 = -9 Simplifying w2 = -9 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 + w)' equal to zero and attempt to solve: Simplifying 3 + w = 0 Solving 3 + w = 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 + w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + w = 0 + -3 w = 0 + -3 Combine like terms: 0 + -3 = -3 w = -3 Simplifying w = -3

Subproblem 3

Set the factor '(-3 + w)' equal to zero and attempt to solve: Simplifying -3 + w = 0 Solving -3 + w = 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 + w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + w = 0 + 3 w = 0 + 3 Combine like terms: 0 + 3 = 3 w = 3 Simplifying w = 3

Solution

w = {-3, 3}

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