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Simplifying (5w + -7)(1 + -1w) = 0 Reorder the terms: (-7 + 5w)(1 + -1w) = 0 Multiply (-7 + 5w) * (1 + -1w) (-7(1 + -1w) + 5w * (1 + -1w)) = 0 ((1 * -7 + -1w * -7) + 5w * (1 + -1w)) = 0 ((-7 + 7w) + 5w * (1 + -1w)) = 0 (-7 + 7w + (1 * 5w + -1w * 5w)) = 0 (-7 + 7w + (5w + -5w2)) = 0 Combine like terms: 7w + 5w = 12w (-7 + 12w + -5w2) = 0 Solving -7 + 12w + -5w2 = 0 Solving for variable 'w'. Factor a trinomial. (-7 + 5w)(1 + -1w) = 0Subproblem 1
Set the factor '(-7 + 5w)' equal to zero and attempt to solve: Simplifying -7 + 5w = 0 Solving -7 + 5w = 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 + 5w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 5w = 0 + 7 5w = 0 + 7 Combine like terms: 0 + 7 = 7 5w = 7 Divide each side by '5'. w = 1.4 Simplifying w = 1.4Subproblem 2
Set the factor '(1 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 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 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Solution
w = {1.4, 1}
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