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Simplifying 0 = 3w2 + -2w + -65 Reorder the terms: 0 = -65 + -2w + 3w2 Solving 0 = -65 + -2w + 3w2 Solving for variable 'w'. Combine like terms: 0 + 65 = 65 65 + 2w + -3w2 = -65 + -2w + 3w2 + 65 + 2w + -3w2 Reorder the terms: 65 + 2w + -3w2 = -65 + 65 + -2w + 2w + 3w2 + -3w2 Combine like terms: -65 + 65 = 0 65 + 2w + -3w2 = 0 + -2w + 2w + 3w2 + -3w2 65 + 2w + -3w2 = -2w + 2w + 3w2 + -3w2 Combine like terms: -2w + 2w = 0 65 + 2w + -3w2 = 0 + 3w2 + -3w2 65 + 2w + -3w2 = 3w2 + -3w2 Combine like terms: 3w2 + -3w2 = 0 65 + 2w + -3w2 = 0 Factor a trinomial. (5 + -1w)(13 + 3w) = 0Subproblem 1
Set the factor '(5 + -1w)' equal to zero and attempt to solve: Simplifying 5 + -1w = 0 Solving 5 + -1w = 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 + -1w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1w = 0 + -5 -1w = 0 + -5 Combine like terms: 0 + -5 = -5 -1w = -5 Divide each side by '-1'. w = 5 Simplifying w = 5Subproblem 2
Set the factor '(13 + 3w)' equal to zero and attempt to solve: Simplifying 13 + 3w = 0 Solving 13 + 3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 3w = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 3w = 0 + -13 3w = 0 + -13 Combine like terms: 0 + -13 = -13 3w = -13 Divide each side by '3'. w = -4.333333333 Simplifying w = -4.333333333Solution
w = {5, -4.333333333}
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