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Simplifying 35 = 3w2 + -8w Reorder the terms: 35 = -8w + 3w2 Solving 35 = -8w + 3w2 Solving for variable 'w'. Reorder the terms: 35 + 8w + -3w2 = -8w + 8w + 3w2 + -3w2 Combine like terms: -8w + 8w = 0 35 + 8w + -3w2 = 0 + 3w2 + -3w2 35 + 8w + -3w2 = 3w2 + -3w2 Combine like terms: 3w2 + -3w2 = 0 35 + 8w + -3w2 = 0 Factor a trinomial. (5 + -1w)(7 + 3w) = 0Subproblem 1
Set the factor '(5 + -1w)' equal to zero and attempt to solve: Simplifying 5 + -1w = 0 Solving 5 + -1w = 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 + -1w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1w = 0 + -5 -1w = 0 + -5 Combine like terms: 0 + -5 = -5 -1w = -5 Divide each side by '-1'. w = 5 Simplifying w = 5Subproblem 2
Set the factor '(7 + 3w)' equal to zero and attempt to solve: Simplifying 7 + 3w = 0 Solving 7 + 3w = 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 + 3w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3w = 0 + -7 3w = 0 + -7 Combine like terms: 0 + -7 = -7 3w = -7 Divide each side by '3'. w = -2.333333333 Simplifying w = -2.333333333Solution
w = {5, -2.333333333}
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