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Simplifying k2 + 80k + 80 = 0 Reorder the terms: 80 + 80k + k2 = 0 Solving 80 + 80k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + 80k + -80 + k2 = 0 + -80 Reorder the terms: 80 + -80 + 80k + k2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + 80k + k2 = 0 + -80 80k + k2 = 0 + -80 Combine like terms: 0 + -80 = -80 80k + k2 = -80 The k term is 80k. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80k + 1600 + k2 = -80 + 1600 Reorder the terms: 1600 + 80k + k2 = -80 + 1600 Combine like terms: -80 + 1600 = 1520 1600 + 80k + k2 = 1520 Factor a perfect square on the left side: (k + 40)(k + 40) = 1520 Calculate the square root of the right side: 38.987177379 Break this problem into two subproblems by setting (k + 40) equal to 38.987177379 and -38.987177379.Subproblem 1
k + 40 = 38.987177379 Simplifying k + 40 = 38.987177379 Reorder the terms: 40 + k = 38.987177379 Solving 40 + k = 38.987177379 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + k = 38.987177379 + -40 Combine like terms: 40 + -40 = 0 0 + k = 38.987177379 + -40 k = 38.987177379 + -40 Combine like terms: 38.987177379 + -40 = -1.012822621 k = -1.012822621 Simplifying k = -1.012822621Subproblem 2
k + 40 = -38.987177379 Simplifying k + 40 = -38.987177379 Reorder the terms: 40 + k = -38.987177379 Solving 40 + k = -38.987177379 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + k = -38.987177379 + -40 Combine like terms: 40 + -40 = 0 0 + k = -38.987177379 + -40 k = -38.987177379 + -40 Combine like terms: -38.987177379 + -40 = -78.987177379 k = -78.987177379 Simplifying k = -78.987177379Solution
The solution to the problem is based on the solutions from the subproblems. k = {-1.012822621, -78.987177379}
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