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Simplifying 8 = w(w + -7) Reorder the terms: 8 = w(-7 + w) 8 = (-7 * w + w * w) 8 = (-7w + w2) Solving 8 = -7w + w2 Solving for variable 'w'. Reorder the terms: 8 + 7w + -1w2 = -7w + 7w + w2 + -1w2 Combine like terms: -7w + 7w = 0 8 + 7w + -1w2 = 0 + w2 + -1w2 8 + 7w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 8 + 7w + -1w2 = 0 Factor a trinomial. (8 + -1w)(1 + w) = 0Subproblem 1
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 = 8Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve: Simplifying 1 + w = 0 Solving 1 + w = 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 + w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + w = 0 + -1 w = 0 + -1 Combine like terms: 0 + -1 = -1 w = -1 Simplifying w = -1Solution
w = {8, -1}
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