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Simplifying (5 + w)(4w + 9) = 0 Reorder the terms: (5 + w)(9 + 4w) = 0 Multiply (5 + w) * (9 + 4w) (5(9 + 4w) + w(9 + 4w)) = 0 ((9 * 5 + 4w * 5) + w(9 + 4w)) = 0 ((45 + 20w) + w(9 + 4w)) = 0 (45 + 20w + (9 * w + 4w * w)) = 0 (45 + 20w + (9w + 4w2)) = 0 Combine like terms: 20w + 9w = 29w (45 + 29w + 4w2) = 0 Solving 45 + 29w + 4w2 = 0 Solving for variable 'w'. Factor a trinomial. (5 + w)(9 + 4w) = 0Subproblem 1
Set the factor '(5 + w)' equal to zero and attempt to solve: Simplifying 5 + w = 0 Solving 5 + w = 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 + w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + w = 0 + -5 w = 0 + -5 Combine like terms: 0 + -5 = -5 w = -5 Simplifying w = -5Subproblem 2
Set the factor '(9 + 4w)' equal to zero and attempt to solve: Simplifying 9 + 4w = 0 Solving 9 + 4w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4w = 0 + -9 4w = 0 + -9 Combine like terms: 0 + -9 = -9 4w = -9 Divide each side by '4'. w = -2.25 Simplifying w = -2.25Solution
w = {-5, -2.25}
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