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Simplifying (2w + -1) * w = 55 Reorder the terms: (-1 + 2w) * w = 55 Reorder the terms for easier multiplication: w(-1 + 2w) = 55 (-1 * w + 2w * w) = 55 (-1w + 2w2) = 55 Solving -1w + 2w2 = 55 Solving for variable 'w'. Reorder the terms: -55 + -1w + 2w2 = 55 + -55 Combine like terms: 55 + -55 = 0 -55 + -1w + 2w2 = 0 Factor a trinomial. (-5 + -1w)(11 + -2w) = 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 '(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 = {-5, 5.5}
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