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Simplifying k2 + 17k = 30 Reorder the terms: 17k + k2 = 30 Solving 17k + k2 = 30 Solving for variable 'k'. Reorder the terms: -30 + 17k + k2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 17k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 17k + 30 + k2 = 0 + 30 Reorder the terms: -30 + 30 + 17k + k2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 17k + k2 = 0 + 30 17k + k2 = 0 + 30 Combine like terms: 0 + 30 = 30 17k + k2 = 30 The k term is 17k. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17k + 72.25 + k2 = 30 + 72.25 Reorder the terms: 72.25 + 17k + k2 = 30 + 72.25 Combine like terms: 30 + 72.25 = 102.25 72.25 + 17k + k2 = 102.25 Factor a perfect square on the left side: (k + 8.5)(k + 8.5) = 102.25 Calculate the square root of the right side: 10.111874208 Break this problem into two subproblems by setting (k + 8.5) equal to 10.111874208 and -10.111874208.Subproblem 1
k + 8.5 = 10.111874208 Simplifying k + 8.5 = 10.111874208 Reorder the terms: 8.5 + k = 10.111874208 Solving 8.5 + k = 10.111874208 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + k = 10.111874208 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + k = 10.111874208 + -8.5 k = 10.111874208 + -8.5 Combine like terms: 10.111874208 + -8.5 = 1.611874208 k = 1.611874208 Simplifying k = 1.611874208Subproblem 2
k + 8.5 = -10.111874208 Simplifying k + 8.5 = -10.111874208 Reorder the terms: 8.5 + k = -10.111874208 Solving 8.5 + k = -10.111874208 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + k = -10.111874208 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + k = -10.111874208 + -8.5 k = -10.111874208 + -8.5 Combine like terms: -10.111874208 + -8.5 = -18.611874208 k = -18.611874208 Simplifying k = -18.611874208Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.611874208, -18.611874208}
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