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Simplifying 50 = (3w + -5) * w Reorder the terms: 50 = (-5 + 3w) * w Reorder the terms for easier multiplication: 50 = w(-5 + 3w) 50 = (-5 * w + 3w * w) 50 = (-5w + 3w2) Solving 50 = -5w + 3w2 Solving for variable 'w'. Reorder the terms: 50 + 5w + -3w2 = -5w + 5w + 3w2 + -3w2 Combine like terms: -5w + 5w = 0 50 + 5w + -3w2 = 0 + 3w2 + -3w2 50 + 5w + -3w2 = 3w2 + -3w2 Combine like terms: 3w2 + -3w2 = 0 50 + 5w + -3w2 = 0 Factor a trinomial. (5 + -1w)(10 + 3w) = 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 '(10 + 3w)' equal to zero and attempt to solve: Simplifying 10 + 3w = 0 Solving 10 + 3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 3w = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 3w = 0 + -10 3w = 0 + -10 Combine like terms: 0 + -10 = -10 3w = -10 Divide each side by '3'. w = -3.333333333 Simplifying w = -3.333333333Solution
w = {5, -3.333333333}
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