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Simplifying 0 = w2 + -10w + -24 Reorder the terms: 0 = -24 + -10w + w2 Solving 0 = -24 + -10w + w2 Solving for variable 'w'. Combine like terms: 0 + 24 = 24 24 + 10w + -1w2 = -24 + -10w + w2 + 24 + 10w + -1w2 Reorder the terms: 24 + 10w + -1w2 = -24 + 24 + -10w + 10w + w2 + -1w2 Combine like terms: -24 + 24 = 0 24 + 10w + -1w2 = 0 + -10w + 10w + w2 + -1w2 24 + 10w + -1w2 = -10w + 10w + w2 + -1w2 Combine like terms: -10w + 10w = 0 24 + 10w + -1w2 = 0 + w2 + -1w2 24 + 10w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 24 + 10w + -1w2 = 0 Factor a trinomial. (12 + -1w)(2 + w) = 0Subproblem 1
Set the factor '(12 + -1w)' equal to zero and attempt to solve: Simplifying 12 + -1w = 0 Solving 12 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1w = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1w = 0 + -12 -1w = 0 + -12 Combine like terms: 0 + -12 = -12 -1w = -12 Divide each side by '-1'. w = 12 Simplifying w = 12Subproblem 2
Set the factor '(2 + w)' equal to zero and attempt to solve: Simplifying 2 + w = 0 Solving 2 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + w = 0 + -2 w = 0 + -2 Combine like terms: 0 + -2 = -2 w = -2 Simplifying w = -2Solution
w = {12, -2}
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