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Simplifying (w + -5)(w + 7) = 0 Reorder the terms: (-5 + w)(w + 7) = 0 Reorder the terms: (-5 + w)(7 + w) = 0 Multiply (-5 + w) * (7 + w) (-5(7 + w) + w(7 + w)) = 0 ((7 * -5 + w * -5) + w(7 + w)) = 0 ((-35 + -5w) + w(7 + w)) = 0 (-35 + -5w + (7 * w + w * w)) = 0 (-35 + -5w + (7w + w2)) = 0 Combine like terms: -5w + 7w = 2w (-35 + 2w + w2) = 0 Solving -35 + 2w + w2 = 0 Solving for variable 'w'. Factor a trinomial. (-7 + -1w)(5 + -1w) = 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 '(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 = {-7, 5}
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