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Simplifying (w + -5)(w + -5) = 2w2 + -5w + 31 Reorder the terms: (-5 + w)(w + -5) = 2w2 + -5w + 31 Reorder the terms: (-5 + w)(-5 + w) = 2w2 + -5w + 31 Multiply (-5 + w) * (-5 + w) (-5(-5 + w) + w(-5 + w)) = 2w2 + -5w + 31 ((-5 * -5 + w * -5) + w(-5 + w)) = 2w2 + -5w + 31 ((25 + -5w) + w(-5 + w)) = 2w2 + -5w + 31 (25 + -5w + (-5 * w + w * w)) = 2w2 + -5w + 31 (25 + -5w + (-5w + w2)) = 2w2 + -5w + 31 Combine like terms: -5w + -5w = -10w (25 + -10w + w2) = 2w2 + -5w + 31 Reorder the terms: 25 + -10w + w2 = 31 + -5w + 2w2 Solving 25 + -10w + w2 = 31 + -5w + 2w2 Solving for variable 'w'. Reorder the terms: 25 + -31 + -10w + 5w + w2 + -2w2 = 31 + -5w + 2w2 + -31 + 5w + -2w2 Combine like terms: 25 + -31 = -6 -6 + -10w + 5w + w2 + -2w2 = 31 + -5w + 2w2 + -31 + 5w + -2w2 Combine like terms: -10w + 5w = -5w -6 + -5w + w2 + -2w2 = 31 + -5w + 2w2 + -31 + 5w + -2w2 Combine like terms: w2 + -2w2 = -1w2 -6 + -5w + -1w2 = 31 + -5w + 2w2 + -31 + 5w + -2w2 Reorder the terms: -6 + -5w + -1w2 = 31 + -31 + -5w + 5w + 2w2 + -2w2 Combine like terms: 31 + -31 = 0 -6 + -5w + -1w2 = 0 + -5w + 5w + 2w2 + -2w2 -6 + -5w + -1w2 = -5w + 5w + 2w2 + -2w2 Combine like terms: -5w + 5w = 0 -6 + -5w + -1w2 = 0 + 2w2 + -2w2 -6 + -5w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -6 + -5w + -1w2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 5w + w2) = 0 Factor a trinomial. -1((3 + w)(2 + w)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + w)' equal to zero and attempt to solve: Simplifying 3 + w = 0 Solving 3 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + w = 0 + -3 w = 0 + -3 Combine like terms: 0 + -3 = -3 w = -3 Simplifying w = -3Subproblem 2
Set the factor '(2 + w)' equal to zero and attempt to solve: Simplifying 2 + w = 0 Solving 2 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + w = 0 + -2 w = 0 + -2 Combine like terms: 0 + -2 = -2 w = -2 Simplifying w = -2Solution
w = {-3, -2}
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