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Simplifying 7k2 + k + -2 = 0 Reorder the terms: -2 + k + 7k2 = 0 Solving -2 + k + 7k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + 0.1428571429k + k2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.1428571429k + 0.2857142857 + k2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 0.1428571429k + k2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 0.1428571429k + k2 = 0 + 0.2857142857 0.1428571429k + k2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 0.1428571429k + k2 = 0.2857142857 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. 0.1428571429k + 0.25 + k2 = 0.2857142857 + 0.25 Reorder the terms: 0.25 + 0.1428571429k + k2 = 0.2857142857 + 0.25 Combine like terms: 0.2857142857 + 0.25 = 0.5357142857 0.25 + 0.1428571429k + k2 = 0.5357142857 Factor a perfect square on the left side: (k + 0.5)(k + 0.5) = 0.5357142857 Calculate the square root of the right side: 0.731925055 Break this problem into two subproblems by setting (k + 0.5) equal to 0.731925055 and -0.731925055.Subproblem 1
k + 0.5 = 0.731925055 Simplifying k + 0.5 = 0.731925055 Reorder the terms: 0.5 + k = 0.731925055 Solving 0.5 + k = 0.731925055 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 = 0.731925055 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + k = 0.731925055 + -0.5 k = 0.731925055 + -0.5 Combine like terms: 0.731925055 + -0.5 = 0.231925055 k = 0.231925055 Simplifying k = 0.231925055Subproblem 2
k + 0.5 = -0.731925055 Simplifying k + 0.5 = -0.731925055 Reorder the terms: 0.5 + k = -0.731925055 Solving 0.5 + k = -0.731925055 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 = -0.731925055 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + k = -0.731925055 + -0.5 k = -0.731925055 + -0.5 Combine like terms: -0.731925055 + -0.5 = -1.231925055 k = -1.231925055 Simplifying k = -1.231925055Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.231925055, -1.231925055}
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