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Simplifying 4k2 + -96 + -1k = 0 Reorder the terms: -96 + -1k + 4k2 = 0 Solving -96 + -1k + 4k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -24 + -0.25k + k2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -0.25k + 24 + k2 = 0 + 24 Reorder the terms: -24 + 24 + -0.25k + k2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -0.25k + k2 = 0 + 24 -0.25k + k2 = 0 + 24 Combine like terms: 0 + 24 = 24 -0.25k + k2 = 24 The k term is -0.25k. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25k + 0.015625 + k2 = 24 + 0.015625 Reorder the terms: 0.015625 + -0.25k + k2 = 24 + 0.015625 Combine like terms: 24 + 0.015625 = 24.015625 0.015625 + -0.25k + k2 = 24.015625 Factor a perfect square on the left side: (k + -0.125)(k + -0.125) = 24.015625 Calculate the square root of the right side: 4.900573946 Break this problem into two subproblems by setting (k + -0.125) equal to 4.900573946 and -4.900573946.Subproblem 1
k + -0.125 = 4.900573946 Simplifying k + -0.125 = 4.900573946 Reorder the terms: -0.125 + k = 4.900573946 Solving -0.125 + k = 4.900573946 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + k = 4.900573946 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + k = 4.900573946 + 0.125 k = 4.900573946 + 0.125 Combine like terms: 4.900573946 + 0.125 = 5.025573946 k = 5.025573946 Simplifying k = 5.025573946Subproblem 2
k + -0.125 = -4.900573946 Simplifying k + -0.125 = -4.900573946 Reorder the terms: -0.125 + k = -4.900573946 Solving -0.125 + k = -4.900573946 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + k = -4.900573946 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + k = -4.900573946 + 0.125 k = -4.900573946 + 0.125 Combine like terms: -4.900573946 + 0.125 = -4.775573946 k = -4.775573946 Simplifying k = -4.775573946Solution
The solution to the problem is based on the solutions from the subproblems. k = {5.025573946, -4.775573946}
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