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Simplifying 403 = (2w + 5)(w) Reorder the terms: 403 = (5 + 2w)(w) Reorder the terms for easier multiplication: 403 = w(5 + 2w) 403 = (5 * w + 2w * w) 403 = (5w + 2w2) Solving 403 = 5w + 2w2 Solving for variable 'w'. Reorder the terms: 403 + -5w + -2w2 = 5w + -5w + 2w2 + -2w2 Combine like terms: 5w + -5w = 0 403 + -5w + -2w2 = 0 + 2w2 + -2w2 403 + -5w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 403 + -5w + -2w2 = 0 Factor a trinomial. (13 + -1w)(31 + 2w) = 0Subproblem 1
Set the factor '(13 + -1w)' equal to zero and attempt to solve: Simplifying 13 + -1w = 0 Solving 13 + -1w = 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 + -1w = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1w = 0 + -13 -1w = 0 + -13 Combine like terms: 0 + -13 = -13 -1w = -13 Divide each side by '-1'. w = 13 Simplifying w = 13Subproblem 2
Set the factor '(31 + 2w)' equal to zero and attempt to solve: Simplifying 31 + 2w = 0 Solving 31 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + 2w = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 2w = 0 + -31 2w = 0 + -31 Combine like terms: 0 + -31 = -31 2w = -31 Divide each side by '2'. w = -15.5 Simplifying w = -15.5Solution
w = {13, -15.5}
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