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Simplifying 406 = 2w2 + 1(w) Reorder the terms: 406 = 1w + 2w2 Solving 406 = 1w + 2w2 Solving for variable 'w'. Reorder the terms: 406 + -1w + -2w2 = 1w + -1w + 2w2 + -2w2 Combine like terms: 1w + -1w = 0 406 + -1w + -2w2 = 0 + 2w2 + -2w2 406 + -1w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 406 + -1w + -2w2 = 0 Factor a trinomial. (14 + -1w)(29 + 2w) = 0Subproblem 1
Set the factor '(14 + -1w)' equal to zero and attempt to solve: Simplifying 14 + -1w = 0 Solving 14 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1w = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1w = 0 + -14 -1w = 0 + -14 Combine like terms: 0 + -14 = -14 -1w = -14 Divide each side by '-1'. w = 14 Simplifying w = 14Subproblem 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 = {14, -14.5}
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