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Simplifying (w + 9)(2w + -1) = 0 Reorder the terms: (9 + w)(2w + -1) = 0 Reorder the terms: (9 + w)(-1 + 2w) = 0 Multiply (9 + w) * (-1 + 2w) (9(-1 + 2w) + w(-1 + 2w)) = 0 ((-1 * 9 + 2w * 9) + w(-1 + 2w)) = 0 ((-9 + 18w) + w(-1 + 2w)) = 0 (-9 + 18w + (-1 * w + 2w * w)) = 0 (-9 + 18w + (-1w + 2w2)) = 0 Combine like terms: 18w + -1w = 17w (-9 + 17w + 2w2) = 0 Solving -9 + 17w + 2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-9 + -1w)(1 + -2w) = 0Subproblem 1
Set the factor '(-9 + -1w)' equal to zero and attempt to solve: Simplifying -9 + -1w = 0 Solving -9 + -1w = 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 + -1w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1w = 0 + 9 -1w = 0 + 9 Combine like terms: 0 + 9 = 9 -1w = 9 Divide each side by '-1'. 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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