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Simplifying 7k2 + -17 = -6k Reorder the terms: -17 + 7k2 = -6k Solving -17 + 7k2 = -6k Solving for variable 'k'. Reorder the terms: -17 + 6k + 7k2 = -6k + 6k Combine like terms: -6k + 6k = 0 -17 + 6k + 7k2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.428571429 + 0.8571428571k + k2 = 0 Move the constant term to the right: Add '2.428571429' to each side of the equation. -2.428571429 + 0.8571428571k + 2.428571429 + k2 = 0 + 2.428571429 Reorder the terms: -2.428571429 + 2.428571429 + 0.8571428571k + k2 = 0 + 2.428571429 Combine like terms: -2.428571429 + 2.428571429 = 0.000000000 0.000000000 + 0.8571428571k + k2 = 0 + 2.428571429 0.8571428571k + k2 = 0 + 2.428571429 Combine like terms: 0 + 2.428571429 = 2.428571429 0.8571428571k + k2 = 2.428571429 The k term is 0.8571428571k. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571k + 0.1836734694 + k2 = 2.428571429 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571k + k2 = 2.428571429 + 0.1836734694 Combine like terms: 2.428571429 + 0.1836734694 = 2.6122448984 0.1836734694 + 0.8571428571k + k2 = 2.6122448984 Factor a perfect square on the left side: (k + 0.4285714286)(k + 0.4285714286) = 2.6122448984 Calculate the square root of the right side: 1.616244071 Break this problem into two subproblems by setting (k + 0.4285714286) equal to 1.616244071 and -1.616244071.Subproblem 1
k + 0.4285714286 = 1.616244071 Simplifying k + 0.4285714286 = 1.616244071 Reorder the terms: 0.4285714286 + k = 1.616244071 Solving 0.4285714286 + k = 1.616244071 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + k = 1.616244071 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + k = 1.616244071 + -0.4285714286 k = 1.616244071 + -0.4285714286 Combine like terms: 1.616244071 + -0.4285714286 = 1.1876726424 k = 1.1876726424 Simplifying k = 1.1876726424Subproblem 2
k + 0.4285714286 = -1.616244071 Simplifying k + 0.4285714286 = -1.616244071 Reorder the terms: 0.4285714286 + k = -1.616244071 Solving 0.4285714286 + k = -1.616244071 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + k = -1.616244071 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + k = -1.616244071 + -0.4285714286 k = -1.616244071 + -0.4285714286 Combine like terms: -1.616244071 + -0.4285714286 = -2.0448154996 k = -2.0448154996 Simplifying k = -2.0448154996Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.1876726424, -2.0448154996}
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