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Simplifying (4w + -1)(8w + 1) = 0 Reorder the terms: (-1 + 4w)(8w + 1) = 0 Reorder the terms: (-1 + 4w)(1 + 8w) = 0 Multiply (-1 + 4w) * (1 + 8w) (-1(1 + 8w) + 4w * (1 + 8w)) = 0 ((1 * -1 + 8w * -1) + 4w * (1 + 8w)) = 0 ((-1 + -8w) + 4w * (1 + 8w)) = 0 (-1 + -8w + (1 * 4w + 8w * 4w)) = 0 (-1 + -8w + (4w + 32w2)) = 0 Combine like terms: -8w + 4w = -4w (-1 + -4w + 32w2) = 0 Solving -1 + -4w + 32w2 = 0 Solving for variable 'w'. Factor a trinomial. (-1 + -8w)(1 + -4w) = 0Subproblem 1
Set the factor '(-1 + -8w)' equal to zero and attempt to solve: Simplifying -1 + -8w = 0 Solving -1 + -8w = 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 + -8w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8w = 0 + 1 -8w = 0 + 1 Combine like terms: 0 + 1 = 1 -8w = 1 Divide each side by '-8'. w = -0.125 Simplifying w = -0.125Subproblem 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 = {-0.125, 0.25}
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