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Simplifying (8 + -1w)(4w + -1) = 0 Reorder the terms: (8 + -1w)(-1 + 4w) = 0 Multiply (8 + -1w) * (-1 + 4w) (8(-1 + 4w) + -1w * (-1 + 4w)) = 0 ((-1 * 8 + 4w * 8) + -1w * (-1 + 4w)) = 0 ((-8 + 32w) + -1w * (-1 + 4w)) = 0 (-8 + 32w + (-1 * -1w + 4w * -1w)) = 0 (-8 + 32w + (1w + -4w2)) = 0 Combine like terms: 32w + 1w = 33w (-8 + 33w + -4w2) = 0 Solving -8 + 33w + -4w2 = 0 Solving for variable 'w'. Factor a trinomial. (-8 + w)(1 + -4w) = 0Subproblem 1
Set the factor '(-8 + w)' equal to zero and attempt to solve: Simplifying -8 + w = 0 Solving -8 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + w = 0 + 8 Combine like terms: -8 + 8 = 0 0 + w = 0 + 8 w = 0 + 8 Combine like terms: 0 + 8 = 8 w = 8 Simplifying w = 8Subproblem 2
Set the factor '(1 + -4w)' equal to zero and attempt to solve: Simplifying 1 + -4w = 0 Solving 1 + -4w = 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 + -4w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4w = 0 + -1 -4w = 0 + -1 Combine like terms: 0 + -1 = -1 -4w = -1 Divide each side by '-4'. w = 0.25 Simplifying w = 0.25Solution
w = {8, 0.25}
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