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Simplifying (6k2 + 2k + 9) + (4k2 + -5k) = 0 Reorder the terms: (9 + 2k + 6k2) + (4k2 + -5k) = 0 Remove parenthesis around (9 + 2k + 6k2) 9 + 2k + 6k2 + (4k2 + -5k) = 0 Reorder the terms: 9 + 2k + 6k2 + (-5k + 4k2) = 0 Remove parenthesis around (-5k + 4k2) 9 + 2k + 6k2 + -5k + 4k2 = 0 Reorder the terms: 9 + 2k + -5k + 6k2 + 4k2 = 0 Combine like terms: 2k + -5k = -3k 9 + -3k + 6k2 + 4k2 = 0 Combine like terms: 6k2 + 4k2 = 10k2 9 + -3k + 10k2 = 0 Solving 9 + -3k + 10k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.9 + -0.3k + k2 = 0.0 Move the constant term to the right: Add '-0.9' to each side of the equation. 0.9 + -0.3k + -0.9 + k2 = 0.0 + -0.9 Reorder the terms: 0.9 + -0.9 + -0.3k + k2 = 0.0 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + -0.3k + k2 = 0.0 + -0.9 -0.3k + k2 = 0.0 + -0.9 Combine like terms: 0.0 + -0.9 = -0.9 -0.3k + k2 = -0.9 The k term is -0.3k. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3k + 0.0225 + k2 = -0.9 + 0.0225 Reorder the terms: 0.0225 + -0.3k + k2 = -0.9 + 0.0225 Combine like terms: -0.9 + 0.0225 = -0.8775 0.0225 + -0.3k + k2 = -0.8775 Factor a perfect square on the left side: (k + -0.15)(k + -0.15) = -0.8775 Can't calculate square root of the right side. The solution to this equation could not be determined.
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