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Simplifying (2w + 7)(w + -5) = 0 Reorder the terms: (7 + 2w)(w + -5) = 0 Reorder the terms: (7 + 2w)(-5 + w) = 0 Multiply (7 + 2w) * (-5 + w) (7(-5 + w) + 2w * (-5 + w)) = 0 ((-5 * 7 + w * 7) + 2w * (-5 + w)) = 0 ((-35 + 7w) + 2w * (-5 + w)) = 0 (-35 + 7w + (-5 * 2w + w * 2w)) = 0 (-35 + 7w + (-10w + 2w2)) = 0 Combine like terms: 7w + -10w = -3w (-35 + -3w + 2w2) = 0 Solving -35 + -3w + 2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-7 + -2w)(5 + -1w) = 0Subproblem 1
Set the factor '(-7 + -2w)' equal to zero and attempt to solve: Simplifying -7 + -2w = 0 Solving -7 + -2w = 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 + -2w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2w = 0 + 7 -2w = 0 + 7 Combine like terms: 0 + 7 = 7 -2w = 7 Divide each side by '-2'. w = -3.5 Simplifying w = -3.5Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve: Simplifying 5 + -1w = 0 Solving 5 + -1w = 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 + -1w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1w = 0 + -5 -1w = 0 + -5 Combine like terms: 0 + -5 = -5 -1w = -5 Divide each side by '-1'. w = 5 Simplifying w = 5Solution
w = {-3.5, 5}
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