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Simplifying 6w = w2 + -27 Reorder the terms: 6w = -27 + w2 Solving 6w = -27 + w2 Solving for variable 'w'. Reorder the terms: 27 + 6w + -1w2 = -27 + w2 + 27 + -1w2 Reorder the terms: 27 + 6w + -1w2 = -27 + 27 + w2 + -1w2 Combine like terms: -27 + 27 = 0 27 + 6w + -1w2 = 0 + w2 + -1w2 27 + 6w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 27 + 6w + -1w2 = 0 Factor a trinomial. (9 + -1w)(3 + w) = 0Subproblem 1
Set the factor '(9 + -1w)' equal to zero and attempt to solve: Simplifying 9 + -1w = 0 Solving 9 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1w = 0 + -9 -1w = 0 + -9 Combine like terms: 0 + -9 = -9 -1w = -9 Divide each side by '-1'. w = 9 Simplifying w = 9Subproblem 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 = {9, -3}
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