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Simplifying (w + 1)(w + -4) = w * w + 9w + 17 Reorder the terms: (1 + w)(w + -4) = w * w + 9w + 17 Reorder the terms: (1 + w)(-4 + w) = w * w + 9w + 17 Multiply (1 + w) * (-4 + w) (1(-4 + w) + w(-4 + w)) = w * w + 9w + 17 ((-4 * 1 + w * 1) + w(-4 + w)) = w * w + 9w + 17 ((-4 + 1w) + w(-4 + w)) = w * w + 9w + 17 (-4 + 1w + (-4 * w + w * w)) = w * w + 9w + 17 (-4 + 1w + (-4w + w2)) = w * w + 9w + 17 Combine like terms: 1w + -4w = -3w (-4 + -3w + w2) = w * w + 9w + 17 Multiply w * w -4 + -3w + w2 = w2 + 9w + 17 Reorder the terms: -4 + -3w + w2 = 17 + 9w + w2 Add '-1w2' to each side of the equation. -4 + -3w + w2 + -1w2 = 17 + 9w + w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -4 + -3w + 0 = 17 + 9w + w2 + -1w2 -4 + -3w = 17 + 9w + w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -4 + -3w = 17 + 9w + 0 -4 + -3w = 17 + 9w Solving -4 + -3w = 17 + 9w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9w' to each side of the equation. -4 + -3w + -9w = 17 + 9w + -9w Combine like terms: -3w + -9w = -12w -4 + -12w = 17 + 9w + -9w Combine like terms: 9w + -9w = 0 -4 + -12w = 17 + 0 -4 + -12w = 17 Add '4' to each side of the equation. -4 + 4 + -12w = 17 + 4 Combine like terms: -4 + 4 = 0 0 + -12w = 17 + 4 -12w = 17 + 4 Combine like terms: 17 + 4 = 21 -12w = 21 Divide each side by '-12'. w = -1.75 Simplifying w = -1.75
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