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Simplifying (5w + -31) * w = 72 Reorder the terms: (-31 + 5w) * w = 72 Reorder the terms for easier multiplication: w(-31 + 5w) = 72 (-31 * w + 5w * w) = 72 (-31w + 5w2) = 72 Solving -31w + 5w2 = 72 Solving for variable 'w'. Reorder the terms: -72 + -31w + 5w2 = 72 + -72 Combine like terms: 72 + -72 = 0 -72 + -31w + 5w2 = 0 Factor a trinomial. (-9 + -5w)(8 + -1w) = 0Subproblem 1
Set the factor '(-9 + -5w)' equal to zero and attempt to solve: Simplifying -9 + -5w = 0 Solving -9 + -5w = 0 Move all terms containing w to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -5w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5w = 0 + 9 -5w = 0 + 9 Combine like terms: 0 + 9 = 9 -5w = 9 Divide each side by '-5'. w = -1.8 Simplifying w = -1.8Subproblem 2
Set the factor '(8 + -1w)' equal to zero and attempt to solve: Simplifying 8 + -1w = 0 Solving 8 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1w = 0 + -8 -1w = 0 + -8 Combine like terms: 0 + -8 = -8 -1w = -8 Divide each side by '-1'. w = 8 Simplifying w = 8Solution
w = {-1.8, 8}
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