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Simplifying 8k2 + k + -11 = 0 Reorder the terms: -11 + k + 8k2 = 0 Solving -11 + k + 8k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.375 + 0.125k + k2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + 0.125k + 1.375 + k2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + 0.125k + k2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + 0.125k + k2 = 0 + 1.375 0.125k + k2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 0.125k + k2 = 1.375 The k term is k. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.125k + 0.25 + k2 = 1.375 + 0.25 Reorder the terms: 0.25 + 0.125k + k2 = 1.375 + 0.25 Combine like terms: 1.375 + 0.25 = 1.625 0.25 + 0.125k + k2 = 1.625 Factor a perfect square on the left side: (k + 0.5)(k + 0.5) = 1.625 Calculate the square root of the right side: 1.274754878 Break this problem into two subproblems by setting (k + 0.5) equal to 1.274754878 and -1.274754878.Subproblem 1
k + 0.5 = 1.274754878 Simplifying k + 0.5 = 1.274754878 Reorder the terms: 0.5 + k = 1.274754878 Solving 0.5 + k = 1.274754878 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + k = 1.274754878 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + k = 1.274754878 + -0.5 k = 1.274754878 + -0.5 Combine like terms: 1.274754878 + -0.5 = 0.774754878 k = 0.774754878 Simplifying k = 0.774754878Subproblem 2
k + 0.5 = -1.274754878 Simplifying k + 0.5 = -1.274754878 Reorder the terms: 0.5 + k = -1.274754878 Solving 0.5 + k = -1.274754878 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + k = -1.274754878 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + k = -1.274754878 + -0.5 k = -1.274754878 + -0.5 Combine like terms: -1.274754878 + -0.5 = -1.774754878 k = -1.774754878 Simplifying k = -1.774754878Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.774754878, -1.774754878}
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