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Simplifying (9 + -1w)(2w + -1) = 0 Reorder the terms: (9 + -1w)(-1 + 2w) = 0 Multiply (9 + -1w) * (-1 + 2w) (9(-1 + 2w) + -1w * (-1 + 2w)) = 0 ((-1 * 9 + 2w * 9) + -1w * (-1 + 2w)) = 0 ((-9 + 18w) + -1w * (-1 + 2w)) = 0 (-9 + 18w + (-1 * -1w + 2w * -1w)) = 0 (-9 + 18w + (1w + -2w2)) = 0 Combine like terms: 18w + 1w = 19w (-9 + 19w + -2w2) = 0 Solving -9 + 19w + -2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-9 + w)(1 + -2w) = 0Subproblem 1
Set the factor '(-9 + w)' equal to zero and attempt to solve: Simplifying -9 + w = 0 Solving -9 + w = 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 + w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + w = 0 + 9 w = 0 + 9 Combine like terms: 0 + 9 = 9 w = 9 Simplifying w = 9Subproblem 2
Set the factor '(1 + -2w)' equal to zero and attempt to solve: Simplifying 1 + -2w = 0 Solving 1 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2w = 0 + -1 -2w = 0 + -1 Combine like terms: 0 + -1 = -1 -2w = -1 Divide each side by '-2'. w = 0.5 Simplifying w = 0.5Solution
w = {9, 0.5}
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