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Simplifying 104 = 2w2 + -3w Reorder the terms: 104 = -3w + 2w2 Solving 104 = -3w + 2w2 Solving for variable 'w'. Reorder the terms: 104 + 3w + -2w2 = -3w + 3w + 2w2 + -2w2 Combine like terms: -3w + 3w = 0 104 + 3w + -2w2 = 0 + 2w2 + -2w2 104 + 3w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 104 + 3w + -2w2 = 0 Factor a trinomial. (8 + -1w)(13 + 2w) = 0Subproblem 1
Set the factor '(8 + -1w)' equal to zero and attempt to solve: Simplifying 8 + -1w = 0 Solving 8 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1w = 0 + -8 -1w = 0 + -8 Combine like terms: 0 + -8 = -8 -1w = -8 Divide each side by '-1'. w = 8 Simplifying w = 8Subproblem 2
Set the factor '(13 + 2w)' equal to zero and attempt to solve: Simplifying 13 + 2w = 0 Solving 13 + 2w = 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 + 2w = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 2w = 0 + -13 2w = 0 + -13 Combine like terms: 0 + -13 = -13 2w = -13 Divide each side by '2'. w = -6.5 Simplifying w = -6.5Solution
w = {8, -6.5}
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