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Simplifying k2 + -4k + -59 = -10 Reorder the terms: -59 + -4k + k2 = -10 Solving -59 + -4k + k2 = -10 Solving for variable 'k'. Reorder the terms: -59 + 10 + -4k + k2 = -10 + 10 Combine like terms: -59 + 10 = -49 -49 + -4k + k2 = -10 + 10 Combine like terms: -10 + 10 = 0 -49 + -4k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -4k + 49 + k2 = 0 + 49 Reorder the terms: -49 + 49 + -4k + k2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -4k + k2 = 0 + 49 -4k + k2 = 0 + 49 Combine like terms: 0 + 49 = 49 -4k + k2 = 49 The k term is -4k. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4k + 4 + k2 = 49 + 4 Reorder the terms: 4 + -4k + k2 = 49 + 4 Combine like terms: 49 + 4 = 53 4 + -4k + k2 = 53 Factor a perfect square on the left side: (k + -2)(k + -2) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (k + -2) equal to 7.280109889 and -7.280109889.Subproblem 1
k + -2 = 7.280109889 Simplifying k + -2 = 7.280109889 Reorder the terms: -2 + k = 7.280109889 Solving -2 + k = 7.280109889 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k = 7.280109889 + 2 Combine like terms: -2 + 2 = 0 0 + k = 7.280109889 + 2 k = 7.280109889 + 2 Combine like terms: 7.280109889 + 2 = 9.280109889 k = 9.280109889 Simplifying k = 9.280109889Subproblem 2
k + -2 = -7.280109889 Simplifying k + -2 = -7.280109889 Reorder the terms: -2 + k = -7.280109889 Solving -2 + k = -7.280109889 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k = -7.280109889 + 2 Combine like terms: -2 + 2 = 0 0 + k = -7.280109889 + 2 k = -7.280109889 + 2 Combine like terms: -7.280109889 + 2 = -5.280109889 k = -5.280109889 Simplifying k = -5.280109889Solution
The solution to the problem is based on the solutions from the subproblems. k = {9.280109889, -5.280109889}
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