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Simplifying 2w2 + -9w + -19 = w2 + -6w + 9 Reorder the terms: -19 + -9w + 2w2 = w2 + -6w + 9 Reorder the terms: -19 + -9w + 2w2 = 9 + -6w + w2 Solving -19 + -9w + 2w2 = 9 + -6w + w2 Solving for variable 'w'. Reorder the terms: -19 + -9 + -9w + 6w + 2w2 + -1w2 = 9 + -6w + w2 + -9 + 6w + -1w2 Combine like terms: -19 + -9 = -28 -28 + -9w + 6w + 2w2 + -1w2 = 9 + -6w + w2 + -9 + 6w + -1w2 Combine like terms: -9w + 6w = -3w -28 + -3w + 2w2 + -1w2 = 9 + -6w + w2 + -9 + 6w + -1w2 Combine like terms: 2w2 + -1w2 = 1w2 -28 + -3w + 1w2 = 9 + -6w + w2 + -9 + 6w + -1w2 Reorder the terms: -28 + -3w + 1w2 = 9 + -9 + -6w + 6w + w2 + -1w2 Combine like terms: 9 + -9 = 0 -28 + -3w + 1w2 = 0 + -6w + 6w + w2 + -1w2 -28 + -3w + 1w2 = -6w + 6w + w2 + -1w2 Combine like terms: -6w + 6w = 0 -28 + -3w + 1w2 = 0 + w2 + -1w2 -28 + -3w + 1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -28 + -3w + 1w2 = 0 Factor a trinomial. (-4 + -1w)(7 + -1w) = 0Subproblem 1
Set the factor '(-4 + -1w)' equal to zero and attempt to solve: Simplifying -4 + -1w = 0 Solving -4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1w = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1w = 0 + 4 -1w = 0 + 4 Combine like terms: 0 + 4 = 4 -1w = 4 Divide each side by '-1'. w = -4 Simplifying w = -4Subproblem 2
Set the factor '(7 + -1w)' equal to zero and attempt to solve: Simplifying 7 + -1w = 0 Solving 7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1w = 0 + -7 -1w = 0 + -7 Combine like terms: 0 + -7 = -7 -1w = -7 Divide each side by '-1'. w = 7 Simplifying w = 7Solution
w = {-4, 7}
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