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Simplifying (w + 3)(w + 3) = 2w2 + 16w + 33 Reorder the terms: (3 + w)(w + 3) = 2w2 + 16w + 33 Reorder the terms: (3 + w)(3 + w) = 2w2 + 16w + 33 Multiply (3 + w) * (3 + w) (3(3 + w) + w(3 + w)) = 2w2 + 16w + 33 ((3 * 3 + w * 3) + w(3 + w)) = 2w2 + 16w + 33 ((9 + 3w) + w(3 + w)) = 2w2 + 16w + 33 (9 + 3w + (3 * w + w * w)) = 2w2 + 16w + 33 (9 + 3w + (3w + w2)) = 2w2 + 16w + 33 Combine like terms: 3w + 3w = 6w (9 + 6w + w2) = 2w2 + 16w + 33 Reorder the terms: 9 + 6w + w2 = 33 + 16w + 2w2 Solving 9 + 6w + w2 = 33 + 16w + 2w2 Solving for variable 'w'. Reorder the terms: 9 + -33 + 6w + -16w + w2 + -2w2 = 33 + 16w + 2w2 + -33 + -16w + -2w2 Combine like terms: 9 + -33 = -24 -24 + 6w + -16w + w2 + -2w2 = 33 + 16w + 2w2 + -33 + -16w + -2w2 Combine like terms: 6w + -16w = -10w -24 + -10w + w2 + -2w2 = 33 + 16w + 2w2 + -33 + -16w + -2w2 Combine like terms: w2 + -2w2 = -1w2 -24 + -10w + -1w2 = 33 + 16w + 2w2 + -33 + -16w + -2w2 Reorder the terms: -24 + -10w + -1w2 = 33 + -33 + 16w + -16w + 2w2 + -2w2 Combine like terms: 33 + -33 = 0 -24 + -10w + -1w2 = 0 + 16w + -16w + 2w2 + -2w2 -24 + -10w + -1w2 = 16w + -16w + 2w2 + -2w2 Combine like terms: 16w + -16w = 0 -24 + -10w + -1w2 = 0 + 2w2 + -2w2 -24 + -10w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -24 + -10w + -1w2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(24 + 10w + w2) = 0 Factor a trinomial. -1((6 + w)(4 + w)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + w)' equal to zero and attempt to solve: Simplifying 6 + w = 0 Solving 6 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + w = 0 + -6 w = 0 + -6 Combine like terms: 0 + -6 = -6 w = -6 Simplifying w = -6Subproblem 2
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 = -4Solution
w = {-6, -4}
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