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Simplifying (2w + -1) * w = 28 Reorder the terms: (-1 + 2w) * w = 28 Reorder the terms for easier multiplication: w(-1 + 2w) = 28 (-1 * w + 2w * w) = 28 (-1w + 2w2) = 28 Solving -1w + 2w2 = 28 Solving for variable 'w'. Reorder the terms: -28 + -1w + 2w2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + -1w + 2w2 = 0 Factor a trinomial. (-7 + -2w)(4 + -1w) = 0Subproblem 1
Set the factor '(-7 + -2w)' equal to zero and attempt to solve: Simplifying -7 + -2w = 0 Solving -7 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2w = 0 + 7 -2w = 0 + 7 Combine like terms: 0 + 7 = 7 -2w = 7 Divide each side by '-2'. w = -3.5 Simplifying w = -3.5Subproblem 2
Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4Solution
w = {-3.5, 4}
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