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Simplifying 3k2 + -6k + -38 = -4 Reorder the terms: -38 + -6k + 3k2 = -4 Solving -38 + -6k + 3k2 = -4 Solving for variable 'k'. Reorder the terms: -38 + 4 + -6k + 3k2 = -4 + 4 Combine like terms: -38 + 4 = -34 -34 + -6k + 3k2 = -4 + 4 Combine like terms: -4 + 4 = 0 -34 + -6k + 3k2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -11.33333333 + -2k + k2 = 0 Move the constant term to the right: Add '11.33333333' to each side of the equation. -11.33333333 + -2k + 11.33333333 + k2 = 0 + 11.33333333 Reorder the terms: -11.33333333 + 11.33333333 + -2k + k2 = 0 + 11.33333333 Combine like terms: -11.33333333 + 11.33333333 = 0.00000000 0.00000000 + -2k + k2 = 0 + 11.33333333 -2k + k2 = 0 + 11.33333333 Combine like terms: 0 + 11.33333333 = 11.33333333 -2k + k2 = 11.33333333 The k term is -2k. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2k + 1 + k2 = 11.33333333 + 1 Reorder the terms: 1 + -2k + k2 = 11.33333333 + 1 Combine like terms: 11.33333333 + 1 = 12.33333333 1 + -2k + k2 = 12.33333333 Factor a perfect square on the left side: (k + -1)(k + -1) = 12.33333333 Calculate the square root of the right side: 3.511884584 Break this problem into two subproblems by setting (k + -1) equal to 3.511884584 and -3.511884584.Subproblem 1
k + -1 = 3.511884584 Simplifying k + -1 = 3.511884584 Reorder the terms: -1 + k = 3.511884584 Solving -1 + k = 3.511884584 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + k = 3.511884584 + 1 Combine like terms: -1 + 1 = 0 0 + k = 3.511884584 + 1 k = 3.511884584 + 1 Combine like terms: 3.511884584 + 1 = 4.511884584 k = 4.511884584 Simplifying k = 4.511884584Subproblem 2
k + -1 = -3.511884584 Simplifying k + -1 = -3.511884584 Reorder the terms: -1 + k = -3.511884584 Solving -1 + k = -3.511884584 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + k = -3.511884584 + 1 Combine like terms: -1 + 1 = 0 0 + k = -3.511884584 + 1 k = -3.511884584 + 1 Combine like terms: -3.511884584 + 1 = -2.511884584 k = -2.511884584 Simplifying k = -2.511884584Solution
The solution to the problem is based on the solutions from the subproblems. k = {4.511884584, -2.511884584}
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