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Simplifying 2w2 = 7w + -5 Reorder the terms: 2w2 = -5 + 7w Solving 2w2 = -5 + 7w Solving for variable 'w'. Reorder the terms: 5 + -7w + 2w2 = -5 + 7w + 5 + -7w Reorder the terms: 5 + -7w + 2w2 = -5 + 5 + 7w + -7w Combine like terms: -5 + 5 = 0 5 + -7w + 2w2 = 0 + 7w + -7w 5 + -7w + 2w2 = 7w + -7w Combine like terms: 7w + -7w = 0 5 + -7w + 2w2 = 0 Factor a trinomial. (1 + -1w)(5 + -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 '(5 + -2w)' equal to zero and attempt to solve: Simplifying 5 + -2w = 0 Solving 5 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2w = 0 + -5 -2w = 0 + -5 Combine like terms: 0 + -5 = -5 -2w = -5 Divide each side by '-2'. w = 2.5 Simplifying w = 2.5Solution
w = {1, 2.5}
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