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Simplifying (3 + 2w) * w = 35 Reorder the terms for easier multiplication: w(3 + 2w) = 35 (3 * w + 2w * w) = 35 (3w + 2w2) = 35 Solving 3w + 2w2 = 35 Solving for variable 'w'. Reorder the terms: -35 + 3w + 2w2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 3w + 2w2 = 0 Factor a trinomial. (-5 + -1w)(7 + -2w) = 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 + -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 = 3.5Solution
w = {-5, 3.5}
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