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Simplifying 2w2 + -11w + 24 = w2 + -36 Reorder the terms: 24 + -11w + 2w2 = w2 + -36 Reorder the terms: 24 + -11w + 2w2 = -36 + w2 Solving 24 + -11w + 2w2 = -36 + w2 Solving for variable 'w'. Reorder the terms: 24 + 36 + -11w + 2w2 + -1w2 = -36 + w2 + 36 + -1w2 Combine like terms: 24 + 36 = 60 60 + -11w + 2w2 + -1w2 = -36 + w2 + 36 + -1w2 Combine like terms: 2w2 + -1w2 = 1w2 60 + -11w + 1w2 = -36 + w2 + 36 + -1w2 Reorder the terms: 60 + -11w + 1w2 = -36 + 36 + w2 + -1w2 Combine like terms: -36 + 36 = 0 60 + -11w + 1w2 = 0 + w2 + -1w2 60 + -11w + 1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 60 + -11w + 1w2 = 0 Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + -11w + -60 + w2 = 0 + -60 Reorder the terms: 60 + -60 + -11w + w2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -11w + w2 = 0 + -60 -11w + w2 = 0 + -60 Combine like terms: 0 + -60 = -60 -11w + w2 = -60 The w term is -11w. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11w + 30.25 + w2 = -60 + 30.25 Reorder the terms: 30.25 + -11w + w2 = -60 + 30.25 Combine like terms: -60 + 30.25 = -29.75 30.25 + -11w + w2 = -29.75 Factor a perfect square on the left side: (w + -5.5)(w + -5.5) = -29.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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