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Simplifying 7w = 2w2 + -4 Reorder the terms: 7w = -4 + 2w2 Solving 7w = -4 + 2w2 Solving for variable 'w'. Reorder the terms: 4 + 7w + -2w2 = -4 + 2w2 + 4 + -2w2 Reorder the terms: 4 + 7w + -2w2 = -4 + 4 + 2w2 + -2w2 Combine like terms: -4 + 4 = 0 4 + 7w + -2w2 = 0 + 2w2 + -2w2 4 + 7w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 4 + 7w + -2w2 = 0 Factor a trinomial. (4 + -1w)(1 + 2w) = 0Subproblem 1
Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4Subproblem 2
Set the factor '(1 + 2w)' equal to zero and attempt to solve: Simplifying 1 + 2w = 0 Solving 1 + 2w = 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 + 2w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2w = 0 + -1 2w = 0 + -1 Combine like terms: 0 + -1 = -1 2w = -1 Divide each side by '2'. w = -0.5 Simplifying w = -0.5Solution
w = {4, -0.5}
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