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Simplifying 0 = 2w2 + -5w + -52 Reorder the terms: 0 = -52 + -5w + 2w2 Solving 0 = -52 + -5w + 2w2 Solving for variable 'w'. Combine like terms: 0 + 52 = 52 52 + 5w + -2w2 = -52 + -5w + 2w2 + 52 + 5w + -2w2 Reorder the terms: 52 + 5w + -2w2 = -52 + 52 + -5w + 5w + 2w2 + -2w2 Combine like terms: -52 + 52 = 0 52 + 5w + -2w2 = 0 + -5w + 5w + 2w2 + -2w2 52 + 5w + -2w2 = -5w + 5w + 2w2 + -2w2 Combine like terms: -5w + 5w = 0 52 + 5w + -2w2 = 0 + 2w2 + -2w2 52 + 5w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 52 + 5w + -2w2 = 0 Factor a trinomial. (13 + -2w)(4 + w) = 0Subproblem 1
Set the factor '(13 + -2w)' equal to zero and attempt to solve: Simplifying 13 + -2w = 0 Solving 13 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -2w = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2w = 0 + -13 -2w = 0 + -13 Combine like terms: 0 + -13 = -13 -2w = -13 Divide each side by '-2'. w = 6.5 Simplifying w = 6.5Subproblem 2
Set the factor '(4 + w)' equal to zero and attempt to solve: Simplifying 4 + w = 0 Solving 4 + w = 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 + w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + w = 0 + -4 w = 0 + -4 Combine like terms: 0 + -4 = -4 w = -4 Simplifying w = -4Solution
w = {6.5, -4}
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