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Simplifying 27 + 20k = -3k(9k + -3) Reorder the terms: 27 + 20k = -3k(-3 + 9k) 27 + 20k = (-3 * -3k + 9k * -3k) 27 + 20k = (9k + -27k2) Solving 27 + 20k = 9k + -27k2 Solving for variable 'k'. Combine like terms: 20k + -9k = 11k 27 + 11k + 27k2 = 9k + -27k2 + -9k + 27k2 Reorder the terms: 27 + 11k + 27k2 = 9k + -9k + -27k2 + 27k2 Combine like terms: 9k + -9k = 0 27 + 11k + 27k2 = 0 + -27k2 + 27k2 27 + 11k + 27k2 = -27k2 + 27k2 Combine like terms: -27k2 + 27k2 = 0 27 + 11k + 27k2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. 1 + 0.4074074074k + k2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.4074074074k + -1 + k2 = 0 + -1 Reorder the terms: 1 + -1 + 0.4074074074k + k2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.4074074074k + k2 = 0 + -1 0.4074074074k + k2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.4074074074k + k2 = -1 The k term is 0.4074074074k. Take half its coefficient (0.2037037037). Square it (0.04149519890) and add it to both sides. Add '0.04149519890' to each side of the equation. 0.4074074074k + 0.04149519890 + k2 = -1 + 0.04149519890 Reorder the terms: 0.04149519890 + 0.4074074074k + k2 = -1 + 0.04149519890 Combine like terms: -1 + 0.04149519890 = -0.9585048011 0.04149519890 + 0.4074074074k + k2 = -0.9585048011 Factor a perfect square on the left side: (k + 0.2037037037)(k + 0.2037037037) = -0.9585048011 Can't calculate square root of the right side. The solution to this equation could not be determined.
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