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Simplifying l2 + 10l + -168 = 0 Reorder the terms: -168 + 10l + l2 = 0 Solving -168 + 10l + l2 = 0 Solving for variable 'l'. Begin completing the square. Move the constant term to the right: Add '168' to each side of the equation. -168 + 10l + 168 + l2 = 0 + 168 Reorder the terms: -168 + 168 + 10l + l2 = 0 + 168 Combine like terms: -168 + 168 = 0 0 + 10l + l2 = 0 + 168 10l + l2 = 0 + 168 Combine like terms: 0 + 168 = 168 10l + l2 = 168 The l term is 10l. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10l + 25 + l2 = 168 + 25 Reorder the terms: 25 + 10l + l2 = 168 + 25 Combine like terms: 168 + 25 = 193 25 + 10l + l2 = 193 Factor a perfect square on the left side: (l + 5)(l + 5) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (l + 5) equal to 13.892443989 and -13.892443989.Subproblem 1
l + 5 = 13.892443989 Simplifying l + 5 = 13.892443989 Reorder the terms: 5 + l = 13.892443989 Solving 5 + l = 13.892443989 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + l = 13.892443989 + -5 Combine like terms: 5 + -5 = 0 0 + l = 13.892443989 + -5 l = 13.892443989 + -5 Combine like terms: 13.892443989 + -5 = 8.892443989 l = 8.892443989 Simplifying l = 8.892443989Subproblem 2
l + 5 = -13.892443989 Simplifying l + 5 = -13.892443989 Reorder the terms: 5 + l = -13.892443989 Solving 5 + l = -13.892443989 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + l = -13.892443989 + -5 Combine like terms: 5 + -5 = 0 0 + l = -13.892443989 + -5 l = -13.892443989 + -5 Combine like terms: -13.892443989 + -5 = -18.892443989 l = -18.892443989 Simplifying l = -18.892443989Solution
The solution to the problem is based on the solutions from the subproblems. l = {8.892443989, -18.892443989}
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