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Simplifying (7 + -1w)(2w + -5) = 0 Reorder the terms: (7 + -1w)(-5 + 2w) = 0 Multiply (7 + -1w) * (-5 + 2w) (7(-5 + 2w) + -1w * (-5 + 2w)) = 0 ((-5 * 7 + 2w * 7) + -1w * (-5 + 2w)) = 0 ((-35 + 14w) + -1w * (-5 + 2w)) = 0 (-35 + 14w + (-5 * -1w + 2w * -1w)) = 0 (-35 + 14w + (5w + -2w2)) = 0 Combine like terms: 14w + 5w = 19w (-35 + 19w + -2w2) = 0 Solving -35 + 19w + -2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-7 + w)(5 + -2w) = 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 '(5 + -2w)' equal to zero and attempt to solve: Simplifying 5 + -2w = 0 Solving 5 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2w = 0 + -5 -2w = 0 + -5 Combine like terms: 0 + -5 = -5 -2w = -5 Divide each side by '-2'. w = 2.5 Simplifying w = 2.5Solution
w = {7, 2.5}
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