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Simplifying w2 + 6w + 9 = 2w2 + 9w + -1 Reorder the terms: 9 + 6w + w2 = 2w2 + 9w + -1 Reorder the terms: 9 + 6w + w2 = -1 + 9w + 2w2 Solving 9 + 6w + w2 = -1 + 9w + 2w2 Solving for variable 'w'. Reorder the terms: 9 + 1 + 6w + -9w + w2 + -2w2 = -1 + 9w + 2w2 + 1 + -9w + -2w2 Combine like terms: 9 + 1 = 10 10 + 6w + -9w + w2 + -2w2 = -1 + 9w + 2w2 + 1 + -9w + -2w2 Combine like terms: 6w + -9w = -3w 10 + -3w + w2 + -2w2 = -1 + 9w + 2w2 + 1 + -9w + -2w2 Combine like terms: w2 + -2w2 = -1w2 10 + -3w + -1w2 = -1 + 9w + 2w2 + 1 + -9w + -2w2 Reorder the terms: 10 + -3w + -1w2 = -1 + 1 + 9w + -9w + 2w2 + -2w2 Combine like terms: -1 + 1 = 0 10 + -3w + -1w2 = 0 + 9w + -9w + 2w2 + -2w2 10 + -3w + -1w2 = 9w + -9w + 2w2 + -2w2 Combine like terms: 9w + -9w = 0 10 + -3w + -1w2 = 0 + 2w2 + -2w2 10 + -3w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 10 + -3w + -1w2 = 0 Factor a trinomial. (2 + -1w)(5 + w) = 0Subproblem 1
Set the factor '(2 + -1w)' equal to zero and attempt to solve: Simplifying 2 + -1w = 0 Solving 2 + -1w = 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 + -1w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w = 0 + -2 -1w = 0 + -2 Combine like terms: 0 + -2 = -2 -1w = -2 Divide each side by '-1'. w = 2 Simplifying w = 2Subproblem 2
Set the factor '(5 + w)' equal to zero and attempt to solve: Simplifying 5 + w = 0 Solving 5 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + w = 0 + -5 w = 0 + -5 Combine like terms: 0 + -5 = -5 w = -5 Simplifying w = -5Solution
w = {2, -5}
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