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Simplifying 493 = 2w2 + -5w Reorder the terms: 493 = -5w + 2w2 Solving 493 = -5w + 2w2 Solving for variable 'w'. Reorder the terms: 493 + 5w + -2w2 = -5w + 5w + 2w2 + -2w2 Combine like terms: -5w + 5w = 0 493 + 5w + -2w2 = 0 + 2w2 + -2w2 493 + 5w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 493 + 5w + -2w2 = 0 Factor a trinomial. (17 + -1w)(29 + 2w) = 0Subproblem 1
Set the factor '(17 + -1w)' equal to zero and attempt to solve: Simplifying 17 + -1w = 0 Solving 17 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -1w = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -1w = 0 + -17 -1w = 0 + -17 Combine like terms: 0 + -17 = -17 -1w = -17 Divide each side by '-1'. w = 17 Simplifying w = 17Subproblem 2
Set the factor '(29 + 2w)' equal to zero and attempt to solve: Simplifying 29 + 2w = 0 Solving 29 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + 2w = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 2w = 0 + -29 2w = 0 + -29 Combine like terms: 0 + -29 = -29 2w = -29 Divide each side by '2'. w = -14.5 Simplifying w = -14.5Solution
w = {17, -14.5}
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