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Simplifying k2 + 8k + -87 = -10 Reorder the terms: -87 + 8k + k2 = -10 Solving -87 + 8k + k2 = -10 Solving for variable 'k'. Reorder the terms: -87 + 10 + 8k + k2 = -10 + 10 Combine like terms: -87 + 10 = -77 -77 + 8k + k2 = -10 + 10 Combine like terms: -10 + 10 = 0 -77 + 8k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + 8k + 77 + k2 = 0 + 77 Reorder the terms: -77 + 77 + 8k + k2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 8k + k2 = 0 + 77 8k + k2 = 0 + 77 Combine like terms: 0 + 77 = 77 8k + k2 = 77 The k term is 8k. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8k + 16 + k2 = 77 + 16 Reorder the terms: 16 + 8k + k2 = 77 + 16 Combine like terms: 77 + 16 = 93 16 + 8k + k2 = 93 Factor a perfect square on the left side: (k + 4)(k + 4) = 93 Calculate the square root of the right side: 9.643650761 Break this problem into two subproblems by setting (k + 4) equal to 9.643650761 and -9.643650761.Subproblem 1
k + 4 = 9.643650761 Simplifying k + 4 = 9.643650761 Reorder the terms: 4 + k = 9.643650761 Solving 4 + k = 9.643650761 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + k = 9.643650761 + -4 Combine like terms: 4 + -4 = 0 0 + k = 9.643650761 + -4 k = 9.643650761 + -4 Combine like terms: 9.643650761 + -4 = 5.643650761 k = 5.643650761 Simplifying k = 5.643650761Subproblem 2
k + 4 = -9.643650761 Simplifying k + 4 = -9.643650761 Reorder the terms: 4 + k = -9.643650761 Solving 4 + k = -9.643650761 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + k = -9.643650761 + -4 Combine like terms: 4 + -4 = 0 0 + k = -9.643650761 + -4 k = -9.643650761 + -4 Combine like terms: -9.643650761 + -4 = -13.643650761 k = -13.643650761 Simplifying k = -13.643650761Solution
The solution to the problem is based on the solutions from the subproblems. k = {5.643650761, -13.643650761}
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