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Simplifying 2k(k + 3) = -15 Reorder the terms: 2k(3 + k) = -15 (3 * 2k + k * 2k) = -15 (6k + 2k2) = -15 Solving 6k + 2k2 = -15 Solving for variable 'k'. Reorder the terms: 15 + 6k + 2k2 = -15 + 15 Combine like terms: -15 + 15 = 0 15 + 6k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + 3k + k2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 3k + -7.5 + k2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 3k + k2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 3k + k2 = 0 + -7.5 3k + k2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 3k + k2 = -7.5 The k term is 3k. 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. 3k + 2.25 + k2 = -7.5 + 2.25 Reorder the terms: 2.25 + 3k + k2 = -7.5 + 2.25 Combine like terms: -7.5 + 2.25 = -5.25 2.25 + 3k + k2 = -5.25 Factor a perfect square on the left side: (k + 1.5)(k + 1.5) = -5.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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