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Simplifying (w + 7)(w + 7) = 2w2 + 6w + 56 Reorder the terms: (7 + w)(w + 7) = 2w2 + 6w + 56 Reorder the terms: (7 + w)(7 + w) = 2w2 + 6w + 56 Multiply (7 + w) * (7 + w) (7(7 + w) + w(7 + w)) = 2w2 + 6w + 56 ((7 * 7 + w * 7) + w(7 + w)) = 2w2 + 6w + 56 ((49 + 7w) + w(7 + w)) = 2w2 + 6w + 56 (49 + 7w + (7 * w + w * w)) = 2w2 + 6w + 56 (49 + 7w + (7w + w2)) = 2w2 + 6w + 56 Combine like terms: 7w + 7w = 14w (49 + 14w + w2) = 2w2 + 6w + 56 Reorder the terms: 49 + 14w + w2 = 56 + 6w + 2w2 Solving 49 + 14w + w2 = 56 + 6w + 2w2 Solving for variable 'w'. Reorder the terms: 49 + -56 + 14w + -6w + w2 + -2w2 = 56 + 6w + 2w2 + -56 + -6w + -2w2 Combine like terms: 49 + -56 = -7 -7 + 14w + -6w + w2 + -2w2 = 56 + 6w + 2w2 + -56 + -6w + -2w2 Combine like terms: 14w + -6w = 8w -7 + 8w + w2 + -2w2 = 56 + 6w + 2w2 + -56 + -6w + -2w2 Combine like terms: w2 + -2w2 = -1w2 -7 + 8w + -1w2 = 56 + 6w + 2w2 + -56 + -6w + -2w2 Reorder the terms: -7 + 8w + -1w2 = 56 + -56 + 6w + -6w + 2w2 + -2w2 Combine like terms: 56 + -56 = 0 -7 + 8w + -1w2 = 0 + 6w + -6w + 2w2 + -2w2 -7 + 8w + -1w2 = 6w + -6w + 2w2 + -2w2 Combine like terms: 6w + -6w = 0 -7 + 8w + -1w2 = 0 + 2w2 + -2w2 -7 + 8w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -7 + 8w + -1w2 = 0 Factor a trinomial. (-7 + w)(1 + -1w) = 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 + -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 = {7, 1}
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