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Simplifying -17w + 40w = 8w2 + 5w Combine like terms: -17w + 40w = 23w 23w = 8w2 + 5w Reorder the terms: 23w = 5w + 8w2 Solving 23w = 5w + 8w2 Solving for variable 'w'. Combine like terms: 23w + -5w = 18w 18w + -8w2 = 5w + 8w2 + -5w + -8w2 Reorder the terms: 18w + -8w2 = 5w + -5w + 8w2 + -8w2 Combine like terms: 5w + -5w = 0 18w + -8w2 = 0 + 8w2 + -8w2 18w + -8w2 = 8w2 + -8w2 Combine like terms: 8w2 + -8w2 = 0 18w + -8w2 = 0 Factor out the Greatest Common Factor (GCF), '2w'. 2w(9 + -4w) = 0 Ignore the factor 2.Subproblem 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 '(9 + -4w)' equal to zero and attempt to solve: Simplifying 9 + -4w = 0 Solving 9 + -4w = 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 + -4w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4w = 0 + -9 -4w = 0 + -9 Combine like terms: 0 + -9 = -9 -4w = -9 Divide each side by '-4'. w = 2.25 Simplifying w = 2.25Solution
w = {0, 2.25}
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