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Simplifying (2w + -5) * w = 150 Reorder the terms: (-5 + 2w) * w = 150 Reorder the terms for easier multiplication: w(-5 + 2w) = 150 (-5 * w + 2w * w) = 150 (-5w + 2w2) = 150 Solving -5w + 2w2 = 150 Solving for variable 'w'. Reorder the terms: -150 + -5w + 2w2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + -5w + 2w2 = 0 Factor a trinomial. (-15 + -2w)(10 + -1w) = 0Subproblem 1
Set the factor '(-15 + -2w)' equal to zero and attempt to solve: Simplifying -15 + -2w = 0 Solving -15 + -2w = 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 + -2w = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -2w = 0 + 15 -2w = 0 + 15 Combine like terms: 0 + 15 = 15 -2w = 15 Divide each side by '-2'. w = -7.5 Simplifying w = -7.5Subproblem 2
Set the factor '(10 + -1w)' equal to zero and attempt to solve: Simplifying 10 + -1w = 0 Solving 10 + -1w = 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 + -1w = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1w = 0 + -10 -1w = 0 + -10 Combine like terms: 0 + -10 = -10 -1w = -10 Divide each side by '-1'. w = 10 Simplifying w = 10Solution
w = {-7.5, 10}
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