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Simplifying 75 = 20w + -1w2 Solving 75 = 20w + -1w2 Solving for variable 'w'. Reorder the terms: 75 + -20w + w2 = 20w + -20w + -1w2 + w2 Combine like terms: 20w + -20w = 0 75 + -20w + w2 = 0 + -1w2 + w2 75 + -20w + w2 = -1w2 + w2 Combine like terms: -1w2 + w2 = 0 75 + -20w + w2 = 0 Factor a trinomial. (5 + -1w)(15 + -1w) = 0Subproblem 1
Set the factor '(5 + -1w)' equal to zero and attempt to solve: Simplifying 5 + -1w = 0 Solving 5 + -1w = 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 + -1w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1w = 0 + -5 -1w = 0 + -5 Combine like terms: 0 + -5 = -5 -1w = -5 Divide each side by '-1'. w = 5 Simplifying w = 5Subproblem 2
Set the factor '(15 + -1w)' equal to zero and attempt to solve: Simplifying 15 + -1w = 0 Solving 15 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1w = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1w = 0 + -15 -1w = 0 + -15 Combine like terms: 0 + -15 = -15 -1w = -15 Divide each side by '-1'. w = 15 Simplifying w = 15Solution
w = {5, 15}
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