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Simplifying (-1w + 7)(5w + -1) = 0 Reorder the terms: (7 + -1w)(5w + -1) = 0 Reorder the terms: (7 + -1w)(-1 + 5w) = 0 Multiply (7 + -1w) * (-1 + 5w) (7(-1 + 5w) + -1w * (-1 + 5w)) = 0 ((-1 * 7 + 5w * 7) + -1w * (-1 + 5w)) = 0 ((-7 + 35w) + -1w * (-1 + 5w)) = 0 (-7 + 35w + (-1 * -1w + 5w * -1w)) = 0 (-7 + 35w + (1w + -5w2)) = 0 Combine like terms: 35w + 1w = 36w (-7 + 36w + -5w2) = 0 Solving -7 + 36w + -5w2 = 0 Solving for variable 'w'. Factor a trinomial. (-7 + w)(1 + -5w) = 0Subproblem 1
Set the factor '(-7 + w)' equal to zero and attempt to solve: Simplifying -7 + w = 0 Solving -7 + w = 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 + w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + w = 0 + 7 w = 0 + 7 Combine like terms: 0 + 7 = 7 w = 7 Simplifying w = 7Subproblem 2
Set the factor '(1 + -5w)' equal to zero and attempt to solve: Simplifying 1 + -5w = 0 Solving 1 + -5w = 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 + -5w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5w = 0 + -1 -5w = 0 + -1 Combine like terms: 0 + -1 = -1 -5w = -1 Divide each side by '-5'. w = 0.2 Simplifying w = 0.2Solution
w = {7, 0.2}
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