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Simplifying (w + -5)(w + -5) = 2w2 + -5w + 29 Reorder the terms: (-5 + w)(w + -5) = 2w2 + -5w + 29 Reorder the terms: (-5 + w)(-5 + w) = 2w2 + -5w + 29 Multiply (-5 + w) * (-5 + w) (-5(-5 + w) + w(-5 + w)) = 2w2 + -5w + 29 ((-5 * -5 + w * -5) + w(-5 + w)) = 2w2 + -5w + 29 ((25 + -5w) + w(-5 + w)) = 2w2 + -5w + 29 (25 + -5w + (-5 * w + w * w)) = 2w2 + -5w + 29 (25 + -5w + (-5w + w2)) = 2w2 + -5w + 29 Combine like terms: -5w + -5w = -10w (25 + -10w + w2) = 2w2 + -5w + 29 Reorder the terms: 25 + -10w + w2 = 29 + -5w + 2w2 Solving 25 + -10w + w2 = 29 + -5w + 2w2 Solving for variable 'w'. Reorder the terms: 25 + -29 + -10w + 5w + w2 + -2w2 = 29 + -5w + 2w2 + -29 + 5w + -2w2 Combine like terms: 25 + -29 = -4 -4 + -10w + 5w + w2 + -2w2 = 29 + -5w + 2w2 + -29 + 5w + -2w2 Combine like terms: -10w + 5w = -5w -4 + -5w + w2 + -2w2 = 29 + -5w + 2w2 + -29 + 5w + -2w2 Combine like terms: w2 + -2w2 = -1w2 -4 + -5w + -1w2 = 29 + -5w + 2w2 + -29 + 5w + -2w2 Reorder the terms: -4 + -5w + -1w2 = 29 + -29 + -5w + 5w + 2w2 + -2w2 Combine like terms: 29 + -29 = 0 -4 + -5w + -1w2 = 0 + -5w + 5w + 2w2 + -2w2 -4 + -5w + -1w2 = -5w + 5w + 2w2 + -2w2 Combine like terms: -5w + 5w = 0 -4 + -5w + -1w2 = 0 + 2w2 + -2w2 -4 + -5w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -4 + -5w + -1w2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 5w + w2) = 0 Factor a trinomial. -1((4 + w)(1 + w)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + w)' equal to zero and attempt to solve: Simplifying 4 + w = 0 Solving 4 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + w = 0 + -4 w = 0 + -4 Combine like terms: 0 + -4 = -4 w = -4 Simplifying w = -4Subproblem 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 = {-4, -1}
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