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Simplifying 2w2 + 3w + 46 = w2 + 16 Reorder the terms: 46 + 3w + 2w2 = w2 + 16 Reorder the terms: 46 + 3w + 2w2 = 16 + w2 Solving 46 + 3w + 2w2 = 16 + w2 Solving for variable 'w'. Reorder the terms: 46 + -16 + 3w + 2w2 + -1w2 = 16 + w2 + -16 + -1w2 Combine like terms: 46 + -16 = 30 30 + 3w + 2w2 + -1w2 = 16 + w2 + -16 + -1w2 Combine like terms: 2w2 + -1w2 = 1w2 30 + 3w + 1w2 = 16 + w2 + -16 + -1w2 Reorder the terms: 30 + 3w + 1w2 = 16 + -16 + w2 + -1w2 Combine like terms: 16 + -16 = 0 30 + 3w + 1w2 = 0 + w2 + -1w2 30 + 3w + 1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 30 + 3w + 1w2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + 3w + -30 + w2 = 0 + -30 Reorder the terms: 30 + -30 + 3w + w2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 3w + w2 = 0 + -30 3w + w2 = 0 + -30 Combine like terms: 0 + -30 = -30 3w + w2 = -30 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = -30 + 2.25 Reorder the terms: 2.25 + 3w + w2 = -30 + 2.25 Combine like terms: -30 + 2.25 = -27.75 2.25 + 3w + w2 = -27.75 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = -27.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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