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Simplifying (w + 8)(w + -2) + (10w + 3)(w + -2) = 0 Reorder the terms: (8 + w)(w + -2) + (10w + 3)(w + -2) = 0 Reorder the terms: (8 + w)(-2 + w) + (10w + 3)(w + -2) = 0 Multiply (8 + w) * (-2 + w) (8(-2 + w) + w(-2 + w)) + (10w + 3)(w + -2) = 0 ((-2 * 8 + w * 8) + w(-2 + w)) + (10w + 3)(w + -2) = 0 ((-16 + 8w) + w(-2 + w)) + (10w + 3)(w + -2) = 0 (-16 + 8w + (-2 * w + w * w)) + (10w + 3)(w + -2) = 0 (-16 + 8w + (-2w + w2)) + (10w + 3)(w + -2) = 0 Combine like terms: 8w + -2w = 6w (-16 + 6w + w2) + (10w + 3)(w + -2) = 0 Reorder the terms: -16 + 6w + w2 + (3 + 10w)(w + -2) = 0 Reorder the terms: -16 + 6w + w2 + (3 + 10w)(-2 + w) = 0 Multiply (3 + 10w) * (-2 + w) -16 + 6w + w2 + (3(-2 + w) + 10w * (-2 + w)) = 0 -16 + 6w + w2 + ((-2 * 3 + w * 3) + 10w * (-2 + w)) = 0 -16 + 6w + w2 + ((-6 + 3w) + 10w * (-2 + w)) = 0 -16 + 6w + w2 + (-6 + 3w + (-2 * 10w + w * 10w)) = 0 -16 + 6w + w2 + (-6 + 3w + (-20w + 10w2)) = 0 Combine like terms: 3w + -20w = -17w -16 + 6w + w2 + (-6 + -17w + 10w2) = 0 Reorder the terms: -16 + -6 + 6w + -17w + w2 + 10w2 = 0 Combine like terms: -16 + -6 = -22 -22 + 6w + -17w + w2 + 10w2 = 0 Combine like terms: 6w + -17w = -11w -22 + -11w + w2 + 10w2 = 0 Combine like terms: w2 + 10w2 = 11w2 -22 + -11w + 11w2 = 0 Solving -22 + -11w + 11w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '11'. 11(-2 + -1w + w2) = 0 Factor a trinomial. 11((-1 + -1w)(2 + -1w)) = 0 Ignore the factor 11.Subproblem 1
Set the factor '(-1 + -1w)' equal to zero and attempt to solve: Simplifying -1 + -1w = 0 Solving -1 + -1w = 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 + -1w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1w = 0 + 1 -1w = 0 + 1 Combine like terms: 0 + 1 = 1 -1w = 1 Divide each side by '-1'. w = -1 Simplifying w = -1Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve: Simplifying 2 + -1w = 0 Solving 2 + -1w = 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 + -1w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w = 0 + -2 -1w = 0 + -2 Combine like terms: 0 + -2 = -2 -1w = -2 Divide each side by '-1'. w = 2 Simplifying w = 2Solution
w = {-1, 2}
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