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Simplifying w2 = 7w + 8 Reorder the terms: w2 = 8 + 7w Solving w2 = 8 + 7w Solving for variable 'w'. Reorder the terms: -8 + -7w + w2 = 8 + 7w + -8 + -7w Reorder the terms: -8 + -7w + w2 = 8 + -8 + 7w + -7w Combine like terms: 8 + -8 = 0 -8 + -7w + w2 = 0 + 7w + -7w -8 + -7w + w2 = 7w + -7w Combine like terms: 7w + -7w = 0 -8 + -7w + w2 = 0 Factor a trinomial. (-1 + -1w)(8 + -1w) = 0Subproblem 1
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 = -1Subproblem 2
Set the factor '(8 + -1w)' equal to zero and attempt to solve: Simplifying 8 + -1w = 0 Solving 8 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1w = 0 + -8 -1w = 0 + -8 Combine like terms: 0 + -8 = -8 -1w = -8 Divide each side by '-1'. w = 8 Simplifying w = 8Solution
w = {-1, 8}
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