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Simplifying l2 + 2l = 100 Reorder the terms: 2l + l2 = 100 Solving 2l + l2 = 100 Solving for variable 'l'. Reorder the terms: -100 + 2l + l2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 2l + l2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 2l + 100 + l2 = 0 + 100 Reorder the terms: -100 + 100 + 2l + l2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 2l + l2 = 0 + 100 2l + l2 = 0 + 100 Combine like terms: 0 + 100 = 100 2l + l2 = 100 The l term is 2l. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2l + 1 + l2 = 100 + 1 Reorder the terms: 1 + 2l + l2 = 100 + 1 Combine like terms: 100 + 1 = 101 1 + 2l + l2 = 101 Factor a perfect square on the left side: (l + 1)(l + 1) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (l + 1) equal to 10.049875621 and -10.049875621.Subproblem 1
l + 1 = 10.049875621 Simplifying l + 1 = 10.049875621 Reorder the terms: 1 + l = 10.049875621 Solving 1 + l = 10.049875621 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + l = 10.049875621 + -1 Combine like terms: 1 + -1 = 0 0 + l = 10.049875621 + -1 l = 10.049875621 + -1 Combine like terms: 10.049875621 + -1 = 9.049875621 l = 9.049875621 Simplifying l = 9.049875621Subproblem 2
l + 1 = -10.049875621 Simplifying l + 1 = -10.049875621 Reorder the terms: 1 + l = -10.049875621 Solving 1 + l = -10.049875621 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + l = -10.049875621 + -1 Combine like terms: 1 + -1 = 0 0 + l = -10.049875621 + -1 l = -10.049875621 + -1 Combine like terms: -10.049875621 + -1 = -11.049875621 l = -11.049875621 Simplifying l = -11.049875621Solution
The solution to the problem is based on the solutions from the subproblems. l = {9.049875621, -11.049875621}
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