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Simplifying k2 + -24k = -6 Reorder the terms: -24k + k2 = -6 Solving -24k + k2 = -6 Solving for variable 'k'. Reorder the terms: 6 + -24k + k2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + -24k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -24k + -6 + k2 = 0 + -6 Reorder the terms: 6 + -6 + -24k + k2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -24k + k2 = 0 + -6 -24k + k2 = 0 + -6 Combine like terms: 0 + -6 = -6 -24k + k2 = -6 The k term is -24k. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24k + 144 + k2 = -6 + 144 Reorder the terms: 144 + -24k + k2 = -6 + 144 Combine like terms: -6 + 144 = 138 144 + -24k + k2 = 138 Factor a perfect square on the left side: (k + -12)(k + -12) = 138 Calculate the square root of the right side: 11.747340124 Break this problem into two subproblems by setting (k + -12) equal to 11.747340124 and -11.747340124.Subproblem 1
k + -12 = 11.747340124 Simplifying k + -12 = 11.747340124 Reorder the terms: -12 + k = 11.747340124 Solving -12 + k = 11.747340124 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + k = 11.747340124 + 12 Combine like terms: -12 + 12 = 0 0 + k = 11.747340124 + 12 k = 11.747340124 + 12 Combine like terms: 11.747340124 + 12 = 23.747340124 k = 23.747340124 Simplifying k = 23.747340124Subproblem 2
k + -12 = -11.747340124 Simplifying k + -12 = -11.747340124 Reorder the terms: -12 + k = -11.747340124 Solving -12 + k = -11.747340124 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + k = -11.747340124 + 12 Combine like terms: -12 + 12 = 0 0 + k = -11.747340124 + 12 k = -11.747340124 + 12 Combine like terms: -11.747340124 + 12 = 0.252659876 k = 0.252659876 Simplifying k = 0.252659876Solution
The solution to the problem is based on the solutions from the subproblems. k = {23.747340124, 0.252659876}
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