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Simplifying 117 = 2w2 + -5w Reorder the terms: 117 = -5w + 2w2 Solving 117 = -5w + 2w2 Solving for variable 'w'. Reorder the terms: 117 + 5w + -2w2 = -5w + 5w + 2w2 + -2w2 Combine like terms: -5w + 5w = 0 117 + 5w + -2w2 = 0 + 2w2 + -2w2 117 + 5w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 117 + 5w + -2w2 = 0 Factor a trinomial. (9 + -1w)(13 + 2w) = 0Subproblem 1
Set the factor '(9 + -1w)' equal to zero and attempt to solve: Simplifying 9 + -1w = 0 Solving 9 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1w = 0 + -9 -1w = 0 + -9 Combine like terms: 0 + -9 = -9 -1w = -9 Divide each side by '-1'. w = 9 Simplifying w = 9Subproblem 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 = {9, -6.5}
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