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Simplifying 7k2 + -1k + -3 = 0 Reorder the terms: -3 + -1k + 7k2 = 0 Solving -3 + -1k + 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'. -0.4285714286 + -0.1428571429k + k2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -0.1428571429k + 0.4285714286 + k2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -0.1428571429k + k2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -0.1428571429k + k2 = 0 + 0.4285714286 -0.1428571429k + k2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -0.1428571429k + k2 = 0.4285714286 The k term is -0.1428571429k. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429k + 0.005102040819 + k2 = 0.4285714286 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429k + k2 = 0.4285714286 + 0.005102040819 Combine like terms: 0.4285714286 + 0.005102040819 = 0.433673469419 0.005102040819 + -0.1428571429k + k2 = 0.433673469419 Factor a perfect square on the left side: (k + -0.07142857145)(k + -0.07142857145) = 0.433673469419 Calculate the square root of the right side: 0.65853889 Break this problem into two subproblems by setting (k + -0.07142857145) equal to 0.65853889 and -0.65853889.Subproblem 1
k + -0.07142857145 = 0.65853889 Simplifying k + -0.07142857145 = 0.65853889 Reorder the terms: -0.07142857145 + k = 0.65853889 Solving -0.07142857145 + k = 0.65853889 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + k = 0.65853889 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + k = 0.65853889 + 0.07142857145 k = 0.65853889 + 0.07142857145 Combine like terms: 0.65853889 + 0.07142857145 = 0.72996746145 k = 0.72996746145 Simplifying k = 0.72996746145Subproblem 2
k + -0.07142857145 = -0.65853889 Simplifying k + -0.07142857145 = -0.65853889 Reorder the terms: -0.07142857145 + k = -0.65853889 Solving -0.07142857145 + k = -0.65853889 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + k = -0.65853889 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + k = -0.65853889 + 0.07142857145 k = -0.65853889 + 0.07142857145 Combine like terms: -0.65853889 + 0.07142857145 = -0.58711031855 k = -0.58711031855 Simplifying k = -0.58711031855Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.72996746145, -0.58711031855}
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