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Simplifying 54 = 2w2 + -3w Reorder the terms: 54 = -3w + 2w2 Solving 54 = -3w + 2w2 Solving for variable 'w'. Reorder the terms: 54 + 3w + -2w2 = -3w + 3w + 2w2 + -2w2 Combine like terms: -3w + 3w = 0 54 + 3w + -2w2 = 0 + 2w2 + -2w2 54 + 3w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 54 + 3w + -2w2 = 0 Factor a trinomial. (6 + -1w)(9 + 2w) = 0Subproblem 1
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 = 6Subproblem 2
Set the factor '(9 + 2w)' equal to zero and attempt to solve: Simplifying 9 + 2w = 0 Solving 9 + 2w = 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 + 2w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2w = 0 + -9 2w = 0 + -9 Combine like terms: 0 + -9 = -9 2w = -9 Divide each side by '2'. w = -4.5 Simplifying w = -4.5Solution
w = {6, -4.5}
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