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Simplifying 2k(k + 5) = -35 Reorder the terms: 2k(5 + k) = -35 (5 * 2k + k * 2k) = -35 (10k + 2k2) = -35 Solving 10k + 2k2 = -35 Solving for variable 'k'. Reorder the terms: 35 + 10k + 2k2 = -35 + 35 Combine like terms: -35 + 35 = 0 35 + 10k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 17.5 + 5k + k2 = 0 Move the constant term to the right: Add '-17.5' to each side of the equation. 17.5 + 5k + -17.5 + k2 = 0 + -17.5 Reorder the terms: 17.5 + -17.5 + 5k + k2 = 0 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + 5k + k2 = 0 + -17.5 5k + k2 = 0 + -17.5 Combine like terms: 0 + -17.5 = -17.5 5k + k2 = -17.5 The k term is 5k. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5k + 6.25 + k2 = -17.5 + 6.25 Reorder the terms: 6.25 + 5k + k2 = -17.5 + 6.25 Combine like terms: -17.5 + 6.25 = -11.25 6.25 + 5k + k2 = -11.25 Factor a perfect square on the left side: (k + 2.5)(k + 2.5) = -11.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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