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Simplifying 2k(k + 7) = -49 Reorder the terms: 2k(7 + k) = -49 (7 * 2k + k * 2k) = -49 (14k + 2k2) = -49 Solving 14k + 2k2 = -49 Solving for variable 'k'. Reorder the terms: 49 + 14k + 2k2 = -49 + 49 Combine like terms: -49 + 49 = 0 49 + 14k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 24.5 + 7k + k2 = 0 Move the constant term to the right: Add '-24.5' to each side of the equation. 24.5 + 7k + -24.5 + k2 = 0 + -24.5 Reorder the terms: 24.5 + -24.5 + 7k + k2 = 0 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + 7k + k2 = 0 + -24.5 7k + k2 = 0 + -24.5 Combine like terms: 0 + -24.5 = -24.5 7k + k2 = -24.5 The k term is 7k. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7k + 12.25 + k2 = -24.5 + 12.25 Reorder the terms: 12.25 + 7k + k2 = -24.5 + 12.25 Combine like terms: -24.5 + 12.25 = -12.25 12.25 + 7k + k2 = -12.25 Factor a perfect square on the left side: (k + 3.5)(k + 3.5) = -12.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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