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Simplifying k2 + -12k + -33 = 8 Reorder the terms: -33 + -12k + k2 = 8 Solving -33 + -12k + k2 = 8 Solving for variable 'k'. Reorder the terms: -33 + -8 + -12k + k2 = 8 + -8 Combine like terms: -33 + -8 = -41 -41 + -12k + k2 = 8 + -8 Combine like terms: 8 + -8 = 0 -41 + -12k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -12k + 41 + k2 = 0 + 41 Reorder the terms: -41 + 41 + -12k + k2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -12k + k2 = 0 + 41 -12k + k2 = 0 + 41 Combine like terms: 0 + 41 = 41 -12k + k2 = 41 The k term is -12k. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12k + 36 + k2 = 41 + 36 Reorder the terms: 36 + -12k + k2 = 41 + 36 Combine like terms: 41 + 36 = 77 36 + -12k + k2 = 77 Factor a perfect square on the left side: (k + -6)(k + -6) = 77 Calculate the square root of the right side: 8.774964387 Break this problem into two subproblems by setting (k + -6) equal to 8.774964387 and -8.774964387.Subproblem 1
k + -6 = 8.774964387 Simplifying k + -6 = 8.774964387 Reorder the terms: -6 + k = 8.774964387 Solving -6 + k = 8.774964387 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + k = 8.774964387 + 6 Combine like terms: -6 + 6 = 0 0 + k = 8.774964387 + 6 k = 8.774964387 + 6 Combine like terms: 8.774964387 + 6 = 14.774964387 k = 14.774964387 Simplifying k = 14.774964387Subproblem 2
k + -6 = -8.774964387 Simplifying k + -6 = -8.774964387 Reorder the terms: -6 + k = -8.774964387 Solving -6 + k = -8.774964387 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + k = -8.774964387 + 6 Combine like terms: -6 + 6 = 0 0 + k = -8.774964387 + 6 k = -8.774964387 + 6 Combine like terms: -8.774964387 + 6 = -2.774964387 k = -2.774964387 Simplifying k = -2.774964387Solution
The solution to the problem is based on the solutions from the subproblems. k = {14.774964387, -2.774964387}
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