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Simplifying 4k2 + 3k + 19 = 9 Reorder the terms: 19 + 3k + 4k2 = 9 Solving 19 + 3k + 4k2 = 9 Solving for variable 'k'. Reorder the terms: 19 + -9 + 3k + 4k2 = 9 + -9 Combine like terms: 19 + -9 = 10 10 + 3k + 4k2 = 9 + -9 Combine like terms: 9 + -9 = 0 10 + 3k + 4k2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.5 + 0.75k + k2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 0.75k + -2.5 + k2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 0.75k + k2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 0.75k + k2 = 0 + -2.5 0.75k + k2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 0.75k + k2 = -2.5 The k term is 0.75k. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75k + 0.140625 + k2 = -2.5 + 0.140625 Reorder the terms: 0.140625 + 0.75k + k2 = -2.5 + 0.140625 Combine like terms: -2.5 + 0.140625 = -2.359375 0.140625 + 0.75k + k2 = -2.359375 Factor a perfect square on the left side: (k + 0.375)(k + 0.375) = -2.359375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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