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Simplifying (2w + -1)(9 + -1w) = 0 Reorder the terms: (-1 + 2w)(9 + -1w) = 0 Multiply (-1 + 2w) * (9 + -1w) (-1(9 + -1w) + 2w * (9 + -1w)) = 0 ((9 * -1 + -1w * -1) + 2w * (9 + -1w)) = 0 ((-9 + 1w) + 2w * (9 + -1w)) = 0 (-9 + 1w + (9 * 2w + -1w * 2w)) = 0 (-9 + 1w + (18w + -2w2)) = 0 Combine like terms: 1w + 18w = 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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