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Simplifying k2 + 13k + -39 = 0 Reorder the terms: -39 + 13k + k2 = 0 Solving -39 + 13k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 13k + 39 + k2 = 0 + 39 Reorder the terms: -39 + 39 + 13k + k2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 13k + k2 = 0 + 39 13k + k2 = 0 + 39 Combine like terms: 0 + 39 = 39 13k + k2 = 39 The k term is 13k. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13k + 42.25 + k2 = 39 + 42.25 Reorder the terms: 42.25 + 13k + k2 = 39 + 42.25 Combine like terms: 39 + 42.25 = 81.25 42.25 + 13k + k2 = 81.25 Factor a perfect square on the left side: (k + 6.5)(k + 6.5) = 81.25 Calculate the square root of the right side: 9.013878189 Break this problem into two subproblems by setting (k + 6.5) equal to 9.013878189 and -9.013878189.Subproblem 1
k + 6.5 = 9.013878189 Simplifying k + 6.5 = 9.013878189 Reorder the terms: 6.5 + k = 9.013878189 Solving 6.5 + k = 9.013878189 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + k = 9.013878189 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + k = 9.013878189 + -6.5 k = 9.013878189 + -6.5 Combine like terms: 9.013878189 + -6.5 = 2.513878189 k = 2.513878189 Simplifying k = 2.513878189Subproblem 2
k + 6.5 = -9.013878189 Simplifying k + 6.5 = -9.013878189 Reorder the terms: 6.5 + k = -9.013878189 Solving 6.5 + k = -9.013878189 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + k = -9.013878189 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + k = -9.013878189 + -6.5 k = -9.013878189 + -6.5 Combine like terms: -9.013878189 + -6.5 = -15.513878189 k = -15.513878189 Simplifying k = -15.513878189Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.513878189, -15.513878189}
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