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Simplifying 7k2 + -20 = -10k Reorder the terms: -20 + 7k2 = -10k Solving -20 + 7k2 = -10k Solving for variable 'k'. Reorder the terms: -20 + 10k + 7k2 = -10k + 10k Combine like terms: -10k + 10k = 0 -20 + 10k + 7k2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.857142857 + 1.428571429k + k2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + 1.428571429k + 2.857142857 + k2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + 1.428571429k + k2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + 1.428571429k + k2 = 0 + 2.857142857 1.428571429k + k2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 1.428571429k + k2 = 2.857142857 The k term is 1.428571429k. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429k + 0.5102040819 + k2 = 2.857142857 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429k + k2 = 2.857142857 + 0.5102040819 Combine like terms: 2.857142857 + 0.5102040819 = 3.3673469389 0.5102040819 + 1.428571429k + k2 = 3.3673469389 Factor a perfect square on the left side: (k + 0.7142857145)(k + 0.7142857145) = 3.3673469389 Calculate the square root of the right side: 1.835033226 Break this problem into two subproblems by setting (k + 0.7142857145) equal to 1.835033226 and -1.835033226.Subproblem 1
k + 0.7142857145 = 1.835033226 Simplifying k + 0.7142857145 = 1.835033226 Reorder the terms: 0.7142857145 + k = 1.835033226 Solving 0.7142857145 + k = 1.835033226 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + k = 1.835033226 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + k = 1.835033226 + -0.7142857145 k = 1.835033226 + -0.7142857145 Combine like terms: 1.835033226 + -0.7142857145 = 1.1207475115 k = 1.1207475115 Simplifying k = 1.1207475115Subproblem 2
k + 0.7142857145 = -1.835033226 Simplifying k + 0.7142857145 = -1.835033226 Reorder the terms: 0.7142857145 + k = -1.835033226 Solving 0.7142857145 + k = -1.835033226 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + k = -1.835033226 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + k = -1.835033226 + -0.7142857145 k = -1.835033226 + -0.7142857145 Combine like terms: -1.835033226 + -0.7142857145 = -2.5493189405 k = -2.5493189405 Simplifying k = -2.5493189405Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.1207475115, -2.5493189405}
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