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Simplifying 5w = w2 + -24 Reorder the terms: 5w = -24 + w2 Solving 5w = -24 + w2 Solving for variable 'w'. Reorder the terms: 24 + 5w + -1w2 = -24 + w2 + 24 + -1w2 Reorder the terms: 24 + 5w + -1w2 = -24 + 24 + w2 + -1w2 Combine like terms: -24 + 24 = 0 24 + 5w + -1w2 = 0 + w2 + -1w2 24 + 5w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 24 + 5w + -1w2 = 0 Factor a trinomial. (8 + -1w)(3 + w) = 0Subproblem 1
Set the factor '(8 + -1w)' equal to zero and attempt to solve: Simplifying 8 + -1w = 0 Solving 8 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1w = 0 + -8 -1w = 0 + -8 Combine like terms: 0 + -8 = -8 -1w = -8 Divide each side by '-1'. w = 8 Simplifying w = 8Subproblem 2
Set the factor '(3 + w)' equal to zero and attempt to solve: Simplifying 3 + w = 0 Solving 3 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + w = 0 + -3 w = 0 + -3 Combine like terms: 0 + -3 = -3 w = -3 Simplifying w = -3Solution
w = {8, -3}
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