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Simplifying (-1l2) + -64l + 2304 = 0 Reorder the terms: 2304 + -64l + (-1l2) = 0 Solving 2304 + -64l + (-1l2) = 0 Solving for variable 'l'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2304 + 64l + l2 = 0 Move the constant term to the right: Add '2304' to each side of the equation. -2304 + 64l + 2304 + l2 = 0 + 2304 Reorder the terms: -2304 + 2304 + 64l + l2 = 0 + 2304 Combine like terms: -2304 + 2304 = 0 0 + 64l + l2 = 0 + 2304 64l + l2 = 0 + 2304 Combine like terms: 0 + 2304 = 2304 64l + l2 = 2304 The l term is 64l. Take half its coefficient (32). Square it (1024) and add it to both sides. Add '1024' to each side of the equation. 64l + 1024 + l2 = 2304 + 1024 Reorder the terms: 1024 + 64l + l2 = 2304 + 1024 Combine like terms: 2304 + 1024 = 3328 1024 + 64l + l2 = 3328 Factor a perfect square on the left side: ((l) + 32)((l) + 32) = 3328 Calculate the square root of the right side: 57.688820407 Break this problem into two subproblems by setting ((l) + 32) equal to 57.688820407 and -57.688820407.Subproblem 1
(l) + 32 = 57.688820407 Simplifying (l) + 32 = 57.688820407 l + 32 = 57.688820407 Reorder the terms: 32 + l = 57.688820407 Solving 32 + l = 57.688820407 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + l = 57.688820407 + -32 Combine like terms: 32 + -32 = 0 0 + l = 57.688820407 + -32 l = 57.688820407 + -32 Combine like terms: 57.688820407 + -32 = 25.688820407 l = 25.688820407 Simplifying l = 25.688820407Subproblem 2
(l) + 32 = -57.688820407 Simplifying (l) + 32 = -57.688820407 l + 32 = -57.688820407 Reorder the terms: 32 + l = -57.688820407 Solving 32 + l = -57.688820407 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + l = -57.688820407 + -32 Combine like terms: 32 + -32 = 0 0 + l = -57.688820407 + -32 l = -57.688820407 + -32 Combine like terms: -57.688820407 + -32 = -89.688820407 l = -89.688820407 Simplifying l = -89.688820407Solution
The solution to the problem is based on the solutions from the subproblems. l = {25.688820407, -89.688820407}
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