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Simplifying 0 = 6w2 + -11w + -35 Reorder the terms: 0 = -35 + -11w + 6w2 Solving 0 = -35 + -11w + 6w2 Solving for variable 'w'. Combine like terms: 0 + 35 = 35 35 + 11w + -6w2 = -35 + -11w + 6w2 + 35 + 11w + -6w2 Reorder the terms: 35 + 11w + -6w2 = -35 + 35 + -11w + 11w + 6w2 + -6w2 Combine like terms: -35 + 35 = 0 35 + 11w + -6w2 = 0 + -11w + 11w + 6w2 + -6w2 35 + 11w + -6w2 = -11w + 11w + 6w2 + -6w2 Combine like terms: -11w + 11w = 0 35 + 11w + -6w2 = 0 + 6w2 + -6w2 35 + 11w + -6w2 = 6w2 + -6w2 Combine like terms: 6w2 + -6w2 = 0 35 + 11w + -6w2 = 0 Factor a trinomial. (7 + -2w)(5 + 3w) = 0Subproblem 1
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 = 3.5Subproblem 2
Set the factor '(5 + 3w)' equal to zero and attempt to solve: Simplifying 5 + 3w = 0 Solving 5 + 3w = 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 + 3w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3w = 0 + -5 3w = 0 + -5 Combine like terms: 0 + -5 = -5 3w = -5 Divide each side by '3'. w = -1.666666667 Simplifying w = -1.666666667Solution
w = {3.5, -1.666666667}
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