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Simplifying 2w2 + -4w + 30 = w2 + 9 Reorder the terms: 30 + -4w + 2w2 = w2 + 9 Reorder the terms: 30 + -4w + 2w2 = 9 + w2 Solving 30 + -4w + 2w2 = 9 + w2 Solving for variable 'w'. Reorder the terms: 30 + -9 + -4w + 2w2 + -1w2 = 9 + w2 + -9 + -1w2 Combine like terms: 30 + -9 = 21 21 + -4w + 2w2 + -1w2 = 9 + w2 + -9 + -1w2 Combine like terms: 2w2 + -1w2 = 1w2 21 + -4w + 1w2 = 9 + w2 + -9 + -1w2 Reorder the terms: 21 + -4w + 1w2 = 9 + -9 + w2 + -1w2 Combine like terms: 9 + -9 = 0 21 + -4w + 1w2 = 0 + w2 + -1w2 21 + -4w + 1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 21 + -4w + 1w2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -4w + -21 + w2 = 0 + -21 Reorder the terms: 21 + -21 + -4w + w2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -4w + w2 = 0 + -21 -4w + w2 = 0 + -21 Combine like terms: 0 + -21 = -21 -4w + w2 = -21 The w term is -4w. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4w + 4 + w2 = -21 + 4 Reorder the terms: 4 + -4w + w2 = -21 + 4 Combine like terms: -21 + 4 = -17 4 + -4w + w2 = -17 Factor a perfect square on the left side: (w + -2)(w + -2) = -17 Can't calculate square root of the right side. The solution to this equation could not be determined.
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