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Simplifying w25 = w Solving w25 = w Solving for variable 'w'. Reorder the terms: -1w + w25 = w + -1w Combine like terms: w + -1w = 0 -1w + w25 = 0 Factor out the Greatest Common Factor (GCF), 'w'. w(-1 + w24) = 0 Factor a difference between two squares. w((1 + w12)(-1 + w12)) = 0 Factor a difference between two squares. w((1 + w12)((1 + w6)(-1 + w6))) = 0 Factor a difference between two squares. w((1 + w12)((1 + w6)((1 + w3)(-1 + w3)))) = 0Subproblem 1
Set the factor 'w' equal to zero and attempt to solve: Simplifying w = 0 Solving w = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w = 0Subproblem 2
Set the factor '(1 + w12)' equal to zero and attempt to solve: Simplifying 1 + w12 = 0 Solving 1 + w12 = 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 + w12 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + w12 = 0 + -1 w12 = 0 + -1 Combine like terms: 0 + -1 = -1 w12 = -1 Simplifying w12 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + w6)' equal to zero and attempt to solve: Simplifying 1 + w6 = 0 Solving 1 + w6 = 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 + w6 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + w6 = 0 + -1 w6 = 0 + -1 Combine like terms: 0 + -1 = -1 w6 = -1 Simplifying w6 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
Set the factor '(1 + w3)' equal to zero and attempt to solve: Simplifying 1 + w3 = 0 Solving 1 + w3 = 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 + w3 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + w3 = 0 + -1 w3 = 0 + -1 Combine like terms: 0 + -1 = -1 w3 = -1 Simplifying w3 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 5
Set the factor '(-1 + w3)' equal to zero and attempt to solve: Simplifying -1 + w3 = 0 Solving -1 + w3 = 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 + w3 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + w3 = 0 + 1 w3 = 0 + 1 Combine like terms: 0 + 1 = 1 w3 = 1 Simplifying w3 = 1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
w = {0}
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