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Simplifying (2w + -5) * w = 33 Reorder the terms: (-5 + 2w) * w = 33 Reorder the terms for easier multiplication: w(-5 + 2w) = 33 (-5 * w + 2w * w) = 33 (-5w + 2w2) = 33 Solving -5w + 2w2 = 33 Solving for variable 'w'. Reorder the terms: -33 + -5w + 2w2 = 33 + -33 Combine like terms: 33 + -33 = 0 -33 + -5w + 2w2 = 0 Factor a trinomial. (-3 + -1w)(11 + -2w) = 0Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve: Simplifying -3 + -1w = 0 Solving -3 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1w = 0 + 3 -1w = 0 + 3 Combine like terms: 0 + 3 = 3 -1w = 3 Divide each side by '-1'. w = -3 Simplifying w = -3Subproblem 2
Set the factor '(11 + -2w)' equal to zero and attempt to solve: Simplifying 11 + -2w = 0 Solving 11 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -2w = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -2w = 0 + -11 -2w = 0 + -11 Combine like terms: 0 + -11 = -11 -2w = -11 Divide each side by '-2'. w = 5.5 Simplifying w = 5.5Solution
w = {-3, 5.5}
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