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Simplifying l2 + 2l + 4 = 192 Reorder the terms: 4 + 2l + l2 = 192 Solving 4 + 2l + l2 = 192 Solving for variable 'l'. Reorder the terms: 4 + -192 + 2l + l2 = 192 + -192 Combine like terms: 4 + -192 = -188 -188 + 2l + l2 = 192 + -192 Combine like terms: 192 + -192 = 0 -188 + 2l + l2 = 0 Begin completing the square. Move the constant term to the right: Add '188' to each side of the equation. -188 + 2l + 188 + l2 = 0 + 188 Reorder the terms: -188 + 188 + 2l + l2 = 0 + 188 Combine like terms: -188 + 188 = 0 0 + 2l + l2 = 0 + 188 2l + l2 = 0 + 188 Combine like terms: 0 + 188 = 188 2l + l2 = 188 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 = 188 + 1 Reorder the terms: 1 + 2l + l2 = 188 + 1 Combine like terms: 188 + 1 = 189 1 + 2l + l2 = 189 Factor a perfect square on the left side: (l + 1)(l + 1) = 189 Calculate the square root of the right side: 13.747727085 Break this problem into two subproblems by setting (l + 1) equal to 13.747727085 and -13.747727085.Subproblem 1
l + 1 = 13.747727085 Simplifying l + 1 = 13.747727085 Reorder the terms: 1 + l = 13.747727085 Solving 1 + l = 13.747727085 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 = 13.747727085 + -1 Combine like terms: 1 + -1 = 0 0 + l = 13.747727085 + -1 l = 13.747727085 + -1 Combine like terms: 13.747727085 + -1 = 12.747727085 l = 12.747727085 Simplifying l = 12.747727085Subproblem 2
l + 1 = -13.747727085 Simplifying l + 1 = -13.747727085 Reorder the terms: 1 + l = -13.747727085 Solving 1 + l = -13.747727085 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 = -13.747727085 + -1 Combine like terms: 1 + -1 = 0 0 + l = -13.747727085 + -1 l = -13.747727085 + -1 Combine like terms: -13.747727085 + -1 = -14.747727085 l = -14.747727085 Simplifying l = -14.747727085Solution
The solution to the problem is based on the solutions from the subproblems. l = {12.747727085, -14.747727085}
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