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Simplifying k2 + -5 = 8k Reorder the terms: -5 + k2 = 8k Solving -5 + k2 = 8k Solving for variable 'k'. Reorder the terms: -5 + -8k + k2 = 8k + -8k Combine like terms: 8k + -8k = 0 -5 + -8k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -8k + 5 + k2 = 0 + 5 Reorder the terms: -5 + 5 + -8k + k2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8k + k2 = 0 + 5 -8k + k2 = 0 + 5 Combine like terms: 0 + 5 = 5 -8k + k2 = 5 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 = 5 + 16 Reorder the terms: 16 + -8k + k2 = 5 + 16 Combine like terms: 5 + 16 = 21 16 + -8k + k2 = 21 Factor a perfect square on the left side: (k + -4)(k + -4) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (k + -4) equal to 4.582575695 and -4.582575695.Subproblem 1
k + -4 = 4.582575695 Simplifying k + -4 = 4.582575695 Reorder the terms: -4 + k = 4.582575695 Solving -4 + k = 4.582575695 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 = 4.582575695 + 4 Combine like terms: -4 + 4 = 0 0 + k = 4.582575695 + 4 k = 4.582575695 + 4 Combine like terms: 4.582575695 + 4 = 8.582575695 k = 8.582575695 Simplifying k = 8.582575695Subproblem 2
k + -4 = -4.582575695 Simplifying k + -4 = -4.582575695 Reorder the terms: -4 + k = -4.582575695 Solving -4 + k = -4.582575695 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 = -4.582575695 + 4 Combine like terms: -4 + 4 = 0 0 + k = -4.582575695 + 4 k = -4.582575695 + 4 Combine like terms: -4.582575695 + 4 = -0.582575695 k = -0.582575695 Simplifying k = -0.582575695Solution
The solution to the problem is based on the solutions from the subproblems. k = {8.582575695, -0.582575695}
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