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Simplifying 7 = -2w2 + 9w Reorder the terms: 7 = 9w + -2w2 Solving 7 = 9w + -2w2 Solving for variable 'w'. Reorder the terms: 7 + -9w + 2w2 = 9w + -9w + -2w2 + 2w2 Combine like terms: 9w + -9w = 0 7 + -9w + 2w2 = 0 + -2w2 + 2w2 7 + -9w + 2w2 = -2w2 + 2w2 Combine like terms: -2w2 + 2w2 = 0 7 + -9w + 2w2 = 0 Factor a trinomial. (1 + -1w)(7 + -2w) = 0Subproblem 1
Set the factor '(1 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Subproblem 2
Set the factor '(7 + -2w)' equal to zero and attempt to solve: Simplifying 7 + -2w = 0 Solving 7 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2w = 0 + -7 -2w = 0 + -7 Combine like terms: 0 + -7 = -7 -2w = -7 Divide each side by '-2'. w = 3.5 Simplifying w = 3.5Solution
w = {1, 3.5}
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