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Simplifying -1l2 + 8l + 96 = 0 Reorder the terms: 96 + 8l + -1l2 = 0 Solving 96 + 8l + -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'. -96 + -8l + l2 = 0 Move the constant term to the right: Add '96' to each side of the equation. -96 + -8l + 96 + l2 = 0 + 96 Reorder the terms: -96 + 96 + -8l + l2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + -8l + l2 = 0 + 96 -8l + l2 = 0 + 96 Combine like terms: 0 + 96 = 96 -8l + l2 = 96 The l term is -8l. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8l + 16 + l2 = 96 + 16 Reorder the terms: 16 + -8l + l2 = 96 + 16 Combine like terms: 96 + 16 = 112 16 + -8l + l2 = 112 Factor a perfect square on the left side: (l + -4)(l + -4) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (l + -4) equal to 10.583005244 and -10.583005244.Subproblem 1
l + -4 = 10.583005244 Simplifying l + -4 = 10.583005244 Reorder the terms: -4 + l = 10.583005244 Solving -4 + l = 10.583005244 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + l = 10.583005244 + 4 Combine like terms: -4 + 4 = 0 0 + l = 10.583005244 + 4 l = 10.583005244 + 4 Combine like terms: 10.583005244 + 4 = 14.583005244 l = 14.583005244 Simplifying l = 14.583005244Subproblem 2
l + -4 = -10.583005244 Simplifying l + -4 = -10.583005244 Reorder the terms: -4 + l = -10.583005244 Solving -4 + l = -10.583005244 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + l = -10.583005244 + 4 Combine like terms: -4 + 4 = 0 0 + l = -10.583005244 + 4 l = -10.583005244 + 4 Combine like terms: -10.583005244 + 4 = -6.583005244 l = -6.583005244 Simplifying l = -6.583005244Solution
The solution to the problem is based on the solutions from the subproblems. l = {14.583005244, -6.583005244}
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