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Simplifying k2 + -20k + 32 = 0 Reorder the terms: 32 + -20k + k2 = 0 Solving 32 + -20k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -20k + -32 + k2 = 0 + -32 Reorder the terms: 32 + -32 + -20k + k2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -20k + k2 = 0 + -32 -20k + k2 = 0 + -32 Combine like terms: 0 + -32 = -32 -20k + k2 = -32 The k term is -20k. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20k + 100 + k2 = -32 + 100 Reorder the terms: 100 + -20k + k2 = -32 + 100 Combine like terms: -32 + 100 = 68 100 + -20k + k2 = 68 Factor a perfect square on the left side: (k + -10)(k + -10) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (k + -10) equal to 8.246211251 and -8.246211251.Subproblem 1
k + -10 = 8.246211251 Simplifying k + -10 = 8.246211251 Reorder the terms: -10 + k = 8.246211251 Solving -10 + k = 8.246211251 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + k = 8.246211251 + 10 Combine like terms: -10 + 10 = 0 0 + k = 8.246211251 + 10 k = 8.246211251 + 10 Combine like terms: 8.246211251 + 10 = 18.246211251 k = 18.246211251 Simplifying k = 18.246211251Subproblem 2
k + -10 = -8.246211251 Simplifying k + -10 = -8.246211251 Reorder the terms: -10 + k = -8.246211251 Solving -10 + k = -8.246211251 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + k = -8.246211251 + 10 Combine like terms: -10 + 10 = 0 0 + k = -8.246211251 + 10 k = -8.246211251 + 10 Combine like terms: -8.246211251 + 10 = 1.753788749 k = 1.753788749 Simplifying k = 1.753788749Solution
The solution to the problem is based on the solutions from the subproblems. k = {18.246211251, 1.753788749}
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