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Simplifying 2w2 + -5w + -17 + -1w2 + 2w + -1 = 0 Reorder the terms: -17 + -1 + -5w + 2w + 2w2 + -1w2 = 0 Combine like terms: -17 + -1 = -18 -18 + -5w + 2w + 2w2 + -1w2 = 0 Combine like terms: -5w + 2w = -3w -18 + -3w + 2w2 + -1w2 = 0 Combine like terms: 2w2 + -1w2 = 1w2 -18 + -3w + 1w2 = 0 Solving -18 + -3w + 1w2 = 0 Solving for variable 'w'. Factor a trinomial. (-3 + -1w)(6 + -1w) = 0Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve: Simplifying -3 + -1w = 0 Solving -3 + -1w = 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 + -1w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1w = 0 + 3 -1w = 0 + 3 Combine like terms: 0 + 3 = 3 -1w = 3 Divide each side by '-1'. w = -3 Simplifying w = -3Subproblem 2
Set the factor '(6 + -1w)' equal to zero and attempt to solve: Simplifying 6 + -1w = 0 Solving 6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1w = 0 + -6 -1w = 0 + -6 Combine like terms: 0 + -6 = -6 -1w = -6 Divide each side by '-1'. w = 6 Simplifying w = 6Solution
w = {-3, 6}
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