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Simplifying 175 = 60w + 4w2 Solving 175 = 60w + 4w2 Solving for variable 'w'. Reorder the terms: 175 + -60w + -4w2 = 60w + -60w + 4w2 + -4w2 Combine like terms: 60w + -60w = 0 175 + -60w + -4w2 = 0 + 4w2 + -4w2 175 + -60w + -4w2 = 4w2 + -4w2 Combine like terms: 4w2 + -4w2 = 0 175 + -60w + -4w2 = 0 Factor a trinomial. (5 + -2w)(35 + 2w) = 0Subproblem 1
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 = 2.5Subproblem 2
Set the factor '(35 + 2w)' equal to zero and attempt to solve: Simplifying 35 + 2w = 0 Solving 35 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + 2w = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 2w = 0 + -35 2w = 0 + -35 Combine like terms: 0 + -35 = -35 2w = -35 Divide each side by '2'. w = -17.5 Simplifying w = -17.5Solution
w = {2.5, -17.5}
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