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Simplifying 91 = (w)(2w + -1) Reorder the terms: 91 = w(-1 + 2w) 91 = (-1 * w + 2w * w) 91 = (-1w + 2w2) Solving 91 = -1w + 2w2 Solving for variable 'w'. Reorder the terms: 91 + w + -2w2 = -1w + w + 2w2 + -2w2 Combine like terms: -1w + w = 0 91 + w + -2w2 = 0 + 2w2 + -2w2 91 + w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 91 + w + -2w2 = 0 Factor a trinomial. (7 + -1w)(13 + 2w) = 0Subproblem 1
Set the factor '(7 + -1w)' equal to zero and attempt to solve: Simplifying 7 + -1w = 0 Solving 7 + -1w = 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 + -1w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1w = 0 + -7 -1w = 0 + -7 Combine like terms: 0 + -7 = -7 -1w = -7 Divide each side by '-1'. w = 7 Simplifying w = 7Subproblem 2
Set the factor '(13 + 2w)' equal to zero and attempt to solve: Simplifying 13 + 2w = 0 Solving 13 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 2w = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 2w = 0 + -13 2w = 0 + -13 Combine like terms: 0 + -13 = -13 2w = -13 Divide each side by '2'. w = -6.5 Simplifying w = -6.5Solution
w = {7, -6.5}
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