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Simplifying 7k2 + -15k + -2 = 0 Reorder the terms: -2 + -15k + 7k2 = 0 Solving -2 + -15k + 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 + -2.142857143k + k2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -2.142857143k + 0.2857142857 + k2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -2.142857143k + k2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -2.142857143k + k2 = 0 + 0.2857142857 -2.142857143k + k2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -2.142857143k + k2 = 0.2857142857 The k term is -2.142857143k. Take half its coefficient (-1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. -2.142857143k + 1.147959185 + k2 = 0.2857142857 + 1.147959185 Reorder the terms: 1.147959185 + -2.142857143k + k2 = 0.2857142857 + 1.147959185 Combine like terms: 0.2857142857 + 1.147959185 = 1.4336734707 1.147959185 + -2.142857143k + k2 = 1.4336734707 Factor a perfect square on the left side: (k + -1.071428572)(k + -1.071428572) = 1.4336734707 Calculate the square root of the right side: 1.197361044 Break this problem into two subproblems by setting (k + -1.071428572) equal to 1.197361044 and -1.197361044.Subproblem 1
k + -1.071428572 = 1.197361044 Simplifying k + -1.071428572 = 1.197361044 Reorder the terms: -1.071428572 + k = 1.197361044 Solving -1.071428572 + k = 1.197361044 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + k = 1.197361044 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + k = 1.197361044 + 1.071428572 k = 1.197361044 + 1.071428572 Combine like terms: 1.197361044 + 1.071428572 = 2.268789616 k = 2.268789616 Simplifying k = 2.268789616Subproblem 2
k + -1.071428572 = -1.197361044 Simplifying k + -1.071428572 = -1.197361044 Reorder the terms: -1.071428572 + k = -1.197361044 Solving -1.071428572 + k = -1.197361044 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + k = -1.197361044 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + k = -1.197361044 + 1.071428572 k = -1.197361044 + 1.071428572 Combine like terms: -1.197361044 + 1.071428572 = -0.125932472 k = -0.125932472 Simplifying k = -0.125932472Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.268789616, -0.125932472}
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