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Simplifying 48w2 + -120w + 75 = 0 Reorder the terms: 75 + -120w + 48w2 = 0 Solving 75 + -120w + 48w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3'. 3(25 + -40w + 16w2) = 0 Factor a trinomial. 3((5 + -4w)(5 + -4w)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -4w)' equal to zero and attempt to solve: Simplifying 5 + -4w = 0 Solving 5 + -4w = 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 + -4w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4w = 0 + -5 -4w = 0 + -5 Combine like terms: 0 + -5 = -5 -4w = -5 Divide each side by '-4'. w = 1.25 Simplifying w = 1.25Subproblem 2
Set the factor '(5 + -4w)' equal to zero and attempt to solve: Simplifying 5 + -4w = 0 Solving 5 + -4w = 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 + -4w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4w = 0 + -5 -4w = 0 + -5 Combine like terms: 0 + -5 = -5 -4w = -5 Divide each side by '-4'. w = 1.25 Simplifying w = 1.25Solution
w = {1.25, 1.25}
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