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Simplifying 0 = w2 + 5w + -456 Reorder the terms: 0 = -456 + 5w + w2 Solving 0 = -456 + 5w + w2 Solving for variable 'w'. Combine like terms: 0 + 456 = 456 456 + -5w + -1w2 = -456 + 5w + w2 + 456 + -5w + -1w2 Reorder the terms: 456 + -5w + -1w2 = -456 + 456 + 5w + -5w + w2 + -1w2 Combine like terms: -456 + 456 = 0 456 + -5w + -1w2 = 0 + 5w + -5w + w2 + -1w2 456 + -5w + -1w2 = 5w + -5w + w2 + -1w2 Combine like terms: 5w + -5w = 0 456 + -5w + -1w2 = 0 + w2 + -1w2 456 + -5w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 456 + -5w + -1w2 = 0 Factor a trinomial. (19 + -1w)(24 + w) = 0Subproblem 1
Set the factor '(19 + -1w)' equal to zero and attempt to solve: Simplifying 19 + -1w = 0 Solving 19 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -1w = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -1w = 0 + -19 -1w = 0 + -19 Combine like terms: 0 + -19 = -19 -1w = -19 Divide each side by '-1'. w = 19 Simplifying w = 19Subproblem 2
Set the factor '(24 + w)' equal to zero and attempt to solve: Simplifying 24 + w = 0 Solving 24 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + w = 0 + -24 Combine like terms: 24 + -24 = 0 0 + w = 0 + -24 w = 0 + -24 Combine like terms: 0 + -24 = -24 w = -24 Simplifying w = -24Solution
w = {19, -24}
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