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Simplifying 5w2 = 40w2 + -80w Reorder the terms: 5w2 = -80w + 40w2 Solving 5w2 = -80w + 40w2 Solving for variable 'w'. Reorder the terms: 80w + 5w2 + -40w2 = -80w + 40w2 + 80w + -40w2 Combine like terms: 5w2 + -40w2 = -35w2 80w + -35w2 = -80w + 40w2 + 80w + -40w2 Reorder the terms: 80w + -35w2 = -80w + 80w + 40w2 + -40w2 Combine like terms: -80w + 80w = 0 80w + -35w2 = 0 + 40w2 + -40w2 80w + -35w2 = 40w2 + -40w2 Combine like terms: 40w2 + -40w2 = 0 80w + -35w2 = 0 Factor out the Greatest Common Factor (GCF), '5w'. 5w(16 + -7w) = 0 Ignore the factor 5.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 '(16 + -7w)' equal to zero and attempt to solve: Simplifying 16 + -7w = 0 Solving 16 + -7w = 0 Move all terms containing w to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -7w = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -7w = 0 + -16 -7w = 0 + -16 Combine like terms: 0 + -16 = -16 -7w = -16 Divide each side by '-7'. w = 2.285714286 Simplifying w = 2.285714286Solution
w = {0, 2.285714286}
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