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Simplifying k2 + -8k + 8 = 0 Reorder the terms: 8 + -8k + k2 = 0 Solving 8 + -8k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -8k + -8 + k2 = 0 + -8 Reorder the terms: 8 + -8 + -8k + k2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -8k + k2 = 0 + -8 -8k + k2 = 0 + -8 Combine like terms: 0 + -8 = -8 -8k + k2 = -8 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 = -8 + 16 Reorder the terms: 16 + -8k + k2 = -8 + 16 Combine like terms: -8 + 16 = 8 16 + -8k + k2 = 8 Factor a perfect square on the left side: (k + -4)(k + -4) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (k + -4) equal to 2.828427125 and -2.828427125.Subproblem 1
k + -4 = 2.828427125 Simplifying k + -4 = 2.828427125 Reorder the terms: -4 + k = 2.828427125 Solving -4 + k = 2.828427125 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 = 2.828427125 + 4 Combine like terms: -4 + 4 = 0 0 + k = 2.828427125 + 4 k = 2.828427125 + 4 Combine like terms: 2.828427125 + 4 = 6.828427125 k = 6.828427125 Simplifying k = 6.828427125Subproblem 2
k + -4 = -2.828427125 Simplifying k + -4 = -2.828427125 Reorder the terms: -4 + k = -2.828427125 Solving -4 + k = -2.828427125 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 = -2.828427125 + 4 Combine like terms: -4 + 4 = 0 0 + k = -2.828427125 + 4 k = -2.828427125 + 4 Combine like terms: -2.828427125 + 4 = 1.171572875 k = 1.171572875 Simplifying k = 1.171572875Solution
The solution to the problem is based on the solutions from the subproblems. k = {6.828427125, 1.171572875}
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