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Simplifying w4 + -15w2 + -16 = 0 Reorder the terms: -16 + -15w2 + w4 = 0 Solving -16 + -15w2 + w4 = 0 Solving for variable 'w'. Factor a trinomial. (-1 + -1w2)(16 + -1w2) = 0 Factor a difference between two squares. (-1 + -1w2)((4 + w)(4 + -1w)) = 0Subproblem 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 '(4 + w)' equal to zero and attempt to solve: Simplifying 4 + w = 0 Solving 4 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + w = 0 + -4 w = 0 + -4 Combine like terms: 0 + -4 = -4 w = -4 Simplifying w = -4Subproblem 3
Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4Solution
w = {-4, 4}
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