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Simplifying k2 + -34k + 144 = 0 Reorder the terms: 144 + -34k + k2 = 0 Solving 144 + -34k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-144' to each side of the equation. 144 + -34k + -144 + k2 = 0 + -144 Reorder the terms: 144 + -144 + -34k + k2 = 0 + -144 Combine like terms: 144 + -144 = 0 0 + -34k + k2 = 0 + -144 -34k + k2 = 0 + -144 Combine like terms: 0 + -144 = -144 -34k + k2 = -144 The k term is -34k. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34k + 289 + k2 = -144 + 289 Reorder the terms: 289 + -34k + k2 = -144 + 289 Combine like terms: -144 + 289 = 145 289 + -34k + k2 = 145 Factor a perfect square on the left side: (k + -17)(k + -17) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (k + -17) equal to 12.041594579 and -12.041594579.Subproblem 1
k + -17 = 12.041594579 Simplifying k + -17 = 12.041594579 Reorder the terms: -17 + k = 12.041594579 Solving -17 + k = 12.041594579 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + k = 12.041594579 + 17 Combine like terms: -17 + 17 = 0 0 + k = 12.041594579 + 17 k = 12.041594579 + 17 Combine like terms: 12.041594579 + 17 = 29.041594579 k = 29.041594579 Simplifying k = 29.041594579Subproblem 2
k + -17 = -12.041594579 Simplifying k + -17 = -12.041594579 Reorder the terms: -17 + k = -12.041594579 Solving -17 + k = -12.041594579 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + k = -12.041594579 + 17 Combine like terms: -17 + 17 = 0 0 + k = -12.041594579 + 17 k = -12.041594579 + 17 Combine like terms: -12.041594579 + 17 = 4.958405421 k = 4.958405421 Simplifying k = 4.958405421Solution
The solution to the problem is based on the solutions from the subproblems. k = {29.041594579, 4.958405421}
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