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Simplifying (5 + -1w)(2w + -9) = 0 Reorder the terms: (5 + -1w)(-9 + 2w) = 0 Multiply (5 + -1w) * (-9 + 2w) (5(-9 + 2w) + -1w * (-9 + 2w)) = 0 ((-9 * 5 + 2w * 5) + -1w * (-9 + 2w)) = 0 ((-45 + 10w) + -1w * (-9 + 2w)) = 0 (-45 + 10w + (-9 * -1w + 2w * -1w)) = 0 (-45 + 10w + (9w + -2w2)) = 0 Combine like terms: 10w + 9w = 19w (-45 + 19w + -2w2) = 0 Solving -45 + 19w + -2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-5 + w)(9 + -2w) = 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 + -2w)' equal to zero and attempt to solve: Simplifying 9 + -2w = 0 Solving 9 + -2w = 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 + -2w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2w = 0 + -9 -2w = 0 + -9 Combine like terms: 0 + -9 = -9 -2w = -9 Divide each side by '-2'. w = 4.5 Simplifying w = 4.5Solution
w = {5, 4.5}
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