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Simplifying 12k + k2 = 32 Solving 12k + k2 = 32 Solving for variable 'k'. Reorder the terms: -32 + 12k + k2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 12k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + 12k + 32 + k2 = 0 + 32 Reorder the terms: -32 + 32 + 12k + k2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 12k + k2 = 0 + 32 12k + k2 = 0 + 32 Combine like terms: 0 + 32 = 32 12k + k2 = 32 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 = 32 + 36 Reorder the terms: 36 + 12k + k2 = 32 + 36 Combine like terms: 32 + 36 = 68 36 + 12k + k2 = 68 Factor a perfect square on the left side: (k + 6)(k + 6) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (k + 6) equal to 8.246211251 and -8.246211251.Subproblem 1
k + 6 = 8.246211251 Simplifying k + 6 = 8.246211251 Reorder the terms: 6 + k = 8.246211251 Solving 6 + k = 8.246211251 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 = 8.246211251 + -6 Combine like terms: 6 + -6 = 0 0 + k = 8.246211251 + -6 k = 8.246211251 + -6 Combine like terms: 8.246211251 + -6 = 2.246211251 k = 2.246211251 Simplifying k = 2.246211251Subproblem 2
k + 6 = -8.246211251 Simplifying k + 6 = -8.246211251 Reorder the terms: 6 + k = -8.246211251 Solving 6 + k = -8.246211251 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 = -8.246211251 + -6 Combine like terms: 6 + -6 = 0 0 + k = -8.246211251 + -6 k = -8.246211251 + -6 Combine like terms: -8.246211251 + -6 = -14.246211251 k = -14.246211251 Simplifying k = -14.246211251Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.246211251, -14.246211251}
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