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Simplifying (w + -4)(w + -4) = 2w2 + -2w + 21 Reorder the terms: (-4 + w)(w + -4) = 2w2 + -2w + 21 Reorder the terms: (-4 + w)(-4 + w) = 2w2 + -2w + 21 Multiply (-4 + w) * (-4 + w) (-4(-4 + w) + w(-4 + w)) = 2w2 + -2w + 21 ((-4 * -4 + w * -4) + w(-4 + w)) = 2w2 + -2w + 21 ((16 + -4w) + w(-4 + w)) = 2w2 + -2w + 21 (16 + -4w + (-4 * w + w * w)) = 2w2 + -2w + 21 (16 + -4w + (-4w + w2)) = 2w2 + -2w + 21 Combine like terms: -4w + -4w = -8w (16 + -8w + w2) = 2w2 + -2w + 21 Reorder the terms: 16 + -8w + w2 = 21 + -2w + 2w2 Solving 16 + -8w + w2 = 21 + -2w + 2w2 Solving for variable 'w'. Reorder the terms: 16 + -21 + -8w + 2w + w2 + -2w2 = 21 + -2w + 2w2 + -21 + 2w + -2w2 Combine like terms: 16 + -21 = -5 -5 + -8w + 2w + w2 + -2w2 = 21 + -2w + 2w2 + -21 + 2w + -2w2 Combine like terms: -8w + 2w = -6w -5 + -6w + w2 + -2w2 = 21 + -2w + 2w2 + -21 + 2w + -2w2 Combine like terms: w2 + -2w2 = -1w2 -5 + -6w + -1w2 = 21 + -2w + 2w2 + -21 + 2w + -2w2 Reorder the terms: -5 + -6w + -1w2 = 21 + -21 + -2w + 2w + 2w2 + -2w2 Combine like terms: 21 + -21 = 0 -5 + -6w + -1w2 = 0 + -2w + 2w + 2w2 + -2w2 -5 + -6w + -1w2 = -2w + 2w + 2w2 + -2w2 Combine like terms: -2w + 2w = 0 -5 + -6w + -1w2 = 0 + 2w2 + -2w2 -5 + -6w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -5 + -6w + -1w2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 6w + w2) = 0 Factor a trinomial. -1((5 + w)(1 + w)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + w)' equal to zero and attempt to solve: Simplifying 5 + w = 0 Solving 5 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + w = 0 + -5 w = 0 + -5 Combine like terms: 0 + -5 = -5 w = -5 Simplifying w = -5Subproblem 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 = {-5, -1}
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