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Simplifying k2 + -16k = 6 Reorder the terms: -16k + k2 = 6 Solving -16k + k2 = 6 Solving for variable 'k'. Reorder the terms: -6 + -16k + k2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -16k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -16k + 6 + k2 = 0 + 6 Reorder the terms: -6 + 6 + -16k + k2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -16k + k2 = 0 + 6 -16k + k2 = 0 + 6 Combine like terms: 0 + 6 = 6 -16k + k2 = 6 The k term is -16k. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16k + 64 + k2 = 6 + 64 Reorder the terms: 64 + -16k + k2 = 6 + 64 Combine like terms: 6 + 64 = 70 64 + -16k + k2 = 70 Factor a perfect square on the left side: (k + -8)(k + -8) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (k + -8) equal to 8.366600265 and -8.366600265.Subproblem 1
k + -8 = 8.366600265 Simplifying k + -8 = 8.366600265 Reorder the terms: -8 + k = 8.366600265 Solving -8 + k = 8.366600265 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + k = 8.366600265 + 8 Combine like terms: -8 + 8 = 0 0 + k = 8.366600265 + 8 k = 8.366600265 + 8 Combine like terms: 8.366600265 + 8 = 16.366600265 k = 16.366600265 Simplifying k = 16.366600265Subproblem 2
k + -8 = -8.366600265 Simplifying k + -8 = -8.366600265 Reorder the terms: -8 + k = -8.366600265 Solving -8 + k = -8.366600265 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + k = -8.366600265 + 8 Combine like terms: -8 + 8 = 0 0 + k = -8.366600265 + 8 k = -8.366600265 + 8 Combine like terms: -8.366600265 + 8 = -0.366600265 k = -0.366600265 Simplifying k = -0.366600265Solution
The solution to the problem is based on the solutions from the subproblems. k = {16.366600265, -0.366600265}
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