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Simplifying 7k2 + -17 = -8k Reorder the terms: -17 + 7k2 = -8k Solving -17 + 7k2 = -8k Solving for variable 'k'. Reorder the terms: -17 + 8k + 7k2 = -8k + 8k Combine like terms: -8k + 8k = 0 -17 + 8k + 7k2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.428571429 + 1.142857143k + k2 = 0 Move the constant term to the right: Add '2.428571429' to each side of the equation. -2.428571429 + 1.142857143k + 2.428571429 + k2 = 0 + 2.428571429 Reorder the terms: -2.428571429 + 2.428571429 + 1.142857143k + k2 = 0 + 2.428571429 Combine like terms: -2.428571429 + 2.428571429 = 0.000000000 0.000000000 + 1.142857143k + k2 = 0 + 2.428571429 1.142857143k + k2 = 0 + 2.428571429 Combine like terms: 0 + 2.428571429 = 2.428571429 1.142857143k + k2 = 2.428571429 The k term is 1.142857143k. Take half its coefficient (0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. 1.142857143k + 0.3265306123 + k2 = 2.428571429 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143k + k2 = 2.428571429 + 0.3265306123 Combine like terms: 2.428571429 + 0.3265306123 = 2.7551020413 0.3265306123 + 1.142857143k + k2 = 2.7551020413 Factor a perfect square on the left side: (k + 0.5714285715)(k + 0.5714285715) = 2.7551020413 Calculate the square root of the right side: 1.659850006 Break this problem into two subproblems by setting (k + 0.5714285715) equal to 1.659850006 and -1.659850006.Subproblem 1
k + 0.5714285715 = 1.659850006 Simplifying k + 0.5714285715 = 1.659850006 Reorder the terms: 0.5714285715 + k = 1.659850006 Solving 0.5714285715 + k = 1.659850006 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + k = 1.659850006 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + k = 1.659850006 + -0.5714285715 k = 1.659850006 + -0.5714285715 Combine like terms: 1.659850006 + -0.5714285715 = 1.0884214345 k = 1.0884214345 Simplifying k = 1.0884214345Subproblem 2
k + 0.5714285715 = -1.659850006 Simplifying k + 0.5714285715 = -1.659850006 Reorder the terms: 0.5714285715 + k = -1.659850006 Solving 0.5714285715 + k = -1.659850006 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + k = -1.659850006 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + k = -1.659850006 + -0.5714285715 k = -1.659850006 + -0.5714285715 Combine like terms: -1.659850006 + -0.5714285715 = -2.2312785775 k = -2.2312785775 Simplifying k = -2.2312785775Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.0884214345, -2.2312785775}
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