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Simplifying w2 + 1 = 2w2 + -9w + 31 Reorder the terms: 1 + w2 = 2w2 + -9w + 31 Reorder the terms: 1 + w2 = 31 + -9w + 2w2 Solving 1 + w2 = 31 + -9w + 2w2 Solving for variable 'w'. Reorder the terms: 1 + -31 + 9w + w2 + -2w2 = 31 + -9w + 2w2 + -31 + 9w + -2w2 Combine like terms: 1 + -31 = -30 -30 + 9w + w2 + -2w2 = 31 + -9w + 2w2 + -31 + 9w + -2w2 Combine like terms: w2 + -2w2 = -1w2 -30 + 9w + -1w2 = 31 + -9w + 2w2 + -31 + 9w + -2w2 Reorder the terms: -30 + 9w + -1w2 = 31 + -31 + -9w + 9w + 2w2 + -2w2 Combine like terms: 31 + -31 = 0 -30 + 9w + -1w2 = 0 + -9w + 9w + 2w2 + -2w2 -30 + 9w + -1w2 = -9w + 9w + 2w2 + -2w2 Combine like terms: -9w + 9w = 0 -30 + 9w + -1w2 = 0 + 2w2 + -2w2 -30 + 9w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -30 + 9w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 30 + -9w + w2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -9w + -30 + w2 = 0 + -30 Reorder the terms: 30 + -30 + -9w + w2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -9w + w2 = 0 + -30 -9w + w2 = 0 + -30 Combine like terms: 0 + -30 = -30 -9w + w2 = -30 The w term is -9w. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9w + 20.25 + w2 = -30 + 20.25 Reorder the terms: 20.25 + -9w + w2 = -30 + 20.25 Combine like terms: -30 + 20.25 = -9.75 20.25 + -9w + w2 = -9.75 Factor a perfect square on the left side: (w + -4.5)(w + -4.5) = -9.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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