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Simplifying k2 + -8k = 43 Reorder the terms: -8k + k2 = 43 Solving -8k + k2 = 43 Solving for variable 'k'. Reorder the terms: -43 + -8k + k2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + -8k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -8k + 43 + k2 = 0 + 43 Reorder the terms: -43 + 43 + -8k + k2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -8k + k2 = 0 + 43 -8k + k2 = 0 + 43 Combine like terms: 0 + 43 = 43 -8k + k2 = 43 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 = 43 + 16 Reorder the terms: 16 + -8k + k2 = 43 + 16 Combine like terms: 43 + 16 = 59 16 + -8k + k2 = 59 Factor a perfect square on the left side: (k + -4)(k + -4) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (k + -4) equal to 7.681145748 and -7.681145748.Subproblem 1
k + -4 = 7.681145748 Simplifying k + -4 = 7.681145748 Reorder the terms: -4 + k = 7.681145748 Solving -4 + k = 7.681145748 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 = 7.681145748 + 4 Combine like terms: -4 + 4 = 0 0 + k = 7.681145748 + 4 k = 7.681145748 + 4 Combine like terms: 7.681145748 + 4 = 11.681145748 k = 11.681145748 Simplifying k = 11.681145748Subproblem 2
k + -4 = -7.681145748 Simplifying k + -4 = -7.681145748 Reorder the terms: -4 + k = -7.681145748 Solving -4 + k = -7.681145748 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 = -7.681145748 + 4 Combine like terms: -4 + 4 = 0 0 + k = -7.681145748 + 4 k = -7.681145748 + 4 Combine like terms: -7.681145748 + 4 = -3.681145748 k = -3.681145748 Simplifying k = -3.681145748Solution
The solution to the problem is based on the solutions from the subproblems. k = {11.681145748, -3.681145748}
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