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Simplifying 10w6 + -35w5 + 25w4 = 0 Reorder the terms: 25w4 + -35w5 + 10w6 = 0 Solving 25w4 + -35w5 + 10w6 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '5w4'. 5w4(5 + -7w + 2w2) = 0 Factor a trinomial. 5w4((1 + -1w)(5 + -2w)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'w4' equal to zero and attempt to solve: Simplifying w4 = 0 Solving w4 = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w4 = 0 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 '(1 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 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 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Subproblem 3
Set the factor '(5 + -2w)' equal to zero and attempt to solve: Simplifying 5 + -2w = 0 Solving 5 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2w = 0 + -5 -2w = 0 + -5 Combine like terms: 0 + -5 = -5 -2w = -5 Divide each side by '-2'. w = 2.5 Simplifying w = 2.5Solution
w = {1, 2.5}
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