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Simplifying w2 + -2w2 + -8w + -7 = 0 Reorder the terms: -7 + -8w + w2 + -2w2 = 0 Combine like terms: w2 + -2w2 = -1w2 -7 + -8w + -1w2 = 0 Solving -7 + -8w + -1w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 8w + w2) = 0 Factor a trinomial. -1((7 + w)(1 + w)) = 0 Ignore the factor -1.Subproblem 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 + 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 = {-7, -1}
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