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Simplifying k2 + -20k = 64 Reorder the terms: -20k + k2 = 64 Solving -20k + k2 = 64 Solving for variable 'k'. Reorder the terms: -64 + -20k + k2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + -20k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -20k + 64 + k2 = 0 + 64 Reorder the terms: -64 + 64 + -20k + k2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -20k + k2 = 0 + 64 -20k + k2 = 0 + 64 Combine like terms: 0 + 64 = 64 -20k + k2 = 64 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 = 64 + 100 Reorder the terms: 100 + -20k + k2 = 64 + 100 Combine like terms: 64 + 100 = 164 100 + -20k + k2 = 164 Factor a perfect square on the left side: (k + -10)(k + -10) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (k + -10) equal to 12.806248475 and -12.806248475.Subproblem 1
k + -10 = 12.806248475 Simplifying k + -10 = 12.806248475 Reorder the terms: -10 + k = 12.806248475 Solving -10 + k = 12.806248475 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 = 12.806248475 + 10 Combine like terms: -10 + 10 = 0 0 + k = 12.806248475 + 10 k = 12.806248475 + 10 Combine like terms: 12.806248475 + 10 = 22.806248475 k = 22.806248475 Simplifying k = 22.806248475Subproblem 2
k + -10 = -12.806248475 Simplifying k + -10 = -12.806248475 Reorder the terms: -10 + k = -12.806248475 Solving -10 + k = -12.806248475 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 = -12.806248475 + 10 Combine like terms: -10 + 10 = 0 0 + k = -12.806248475 + 10 k = -12.806248475 + 10 Combine like terms: -12.806248475 + 10 = -2.806248475 k = -2.806248475 Simplifying k = -2.806248475Solution
The solution to the problem is based on the solutions from the subproblems. k = {22.806248475, -2.806248475}
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