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Simplifying (4w + -1)(7 + w) = 0 Reorder the terms: (-1 + 4w)(7 + w) = 0 Multiply (-1 + 4w) * (7 + w) (-1(7 + w) + 4w * (7 + w)) = 0 ((7 * -1 + w * -1) + 4w * (7 + w)) = 0 ((-7 + -1w) + 4w * (7 + w)) = 0 (-7 + -1w + (7 * 4w + w * 4w)) = 0 (-7 + -1w + (28w + 4w2)) = 0 Combine like terms: -1w + 28w = 27w (-7 + 27w + 4w2) = 0 Solving -7 + 27w + 4w2 = 0 Solving for variable 'w'. Factor a trinomial. (-7 + -1w)(1 + -4w) = 0Subproblem 1
Set the factor '(-7 + -1w)' equal to zero and attempt to solve: Simplifying -7 + -1w = 0 Solving -7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1w = 0 + 7 -1w = 0 + 7 Combine like terms: 0 + 7 = 7 -1w = 7 Divide each side by '-1'. w = -7 Simplifying w = -7Subproblem 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 = {-7, 0.25}
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