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Simplifying (-3w2 + -9w + 8) + (2w2 + -7w + 8) + -1(-5w2 + -3w + 5) = 0 Reorder the terms: (8 + -9w + -3w2) + (2w2 + -7w + 8) + -1(-5w2 + -3w + 5) = 0 Remove parenthesis around (8 + -9w + -3w2) 8 + -9w + -3w2 + (2w2 + -7w + 8) + -1(-5w2 + -3w + 5) = 0 Reorder the terms: 8 + -9w + -3w2 + (8 + -7w + 2w2) + -1(-5w2 + -3w + 5) = 0 Remove parenthesis around (8 + -7w + 2w2) 8 + -9w + -3w2 + 8 + -7w + 2w2 + -1(-5w2 + -3w + 5) = 0 Reorder the terms: 8 + -9w + -3w2 + 8 + -7w + 2w2 + -1(5 + -3w + -5w2) = 0 8 + -9w + -3w2 + 8 + -7w + 2w2 + (5 * -1 + -3w * -1 + -5w2 * -1) = 0 8 + -9w + -3w2 + 8 + -7w + 2w2 + (-5 + 3w + 5w2) = 0 Reorder the terms: 8 + 8 + -5 + -9w + -7w + 3w + -3w2 + 2w2 + 5w2 = 0 Combine like terms: 8 + 8 = 16 16 + -5 + -9w + -7w + 3w + -3w2 + 2w2 + 5w2 = 0 Combine like terms: 16 + -5 = 11 11 + -9w + -7w + 3w + -3w2 + 2w2 + 5w2 = 0 Combine like terms: -9w + -7w = -16w 11 + -16w + 3w + -3w2 + 2w2 + 5w2 = 0 Combine like terms: -16w + 3w = -13w 11 + -13w + -3w2 + 2w2 + 5w2 = 0 Combine like terms: -3w2 + 2w2 = -1w2 11 + -13w + -1w2 + 5w2 = 0 Combine like terms: -1w2 + 5w2 = 4w2 11 + -13w + 4w2 = 0 Solving 11 + -13w + 4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.75 + -3.25w + w2 = 0 Move the constant term to the right: Add '-2.75' to each side of the equation. 2.75 + -3.25w + -2.75 + w2 = 0 + -2.75 Reorder the terms: 2.75 + -2.75 + -3.25w + w2 = 0 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + -3.25w + w2 = 0 + -2.75 -3.25w + w2 = 0 + -2.75 Combine like terms: 0 + -2.75 = -2.75 -3.25w + w2 = -2.75 The w term is -3.25w. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25w + 2.640625 + w2 = -2.75 + 2.640625 Reorder the terms: 2.640625 + -3.25w + w2 = -2.75 + 2.640625 Combine like terms: -2.75 + 2.640625 = -0.109375 2.640625 + -3.25w + w2 = -0.109375 Factor a perfect square on the left side: (w + -1.625)(w + -1.625) = -0.109375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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