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Simplifying 0 = l2 + 2l + -64 Reorder the terms: 0 = -64 + 2l + l2 Solving 0 = -64 + 2l + l2 Solving for variable 'l'. Combine like terms: 0 + 64 = 64 64 + -2l + -1l2 = -64 + 2l + l2 + 64 + -2l + -1l2 Reorder the terms: 64 + -2l + -1l2 = -64 + 64 + 2l + -2l + l2 + -1l2 Combine like terms: -64 + 64 = 0 64 + -2l + -1l2 = 0 + 2l + -2l + l2 + -1l2 64 + -2l + -1l2 = 2l + -2l + l2 + -1l2 Combine like terms: 2l + -2l = 0 64 + -2l + -1l2 = 0 + l2 + -1l2 64 + -2l + -1l2 = l2 + -1l2 Combine like terms: l2 + -1l2 = 0 64 + -2l + -1l2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -64 + 2l + l2 = 0 Move the constant term to the right: Add '64' to each side of the equation. -64 + 2l + 64 + l2 = 0 + 64 Reorder the terms: -64 + 64 + 2l + l2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 2l + l2 = 0 + 64 2l + l2 = 0 + 64 Combine like terms: 0 + 64 = 64 2l + l2 = 64 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 = 64 + 1 Reorder the terms: 1 + 2l + l2 = 64 + 1 Combine like terms: 64 + 1 = 65 1 + 2l + l2 = 65 Factor a perfect square on the left side: (l + 1)(l + 1) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (l + 1) equal to 8.062257748 and -8.062257748.Subproblem 1
l + 1 = 8.062257748 Simplifying l + 1 = 8.062257748 Reorder the terms: 1 + l = 8.062257748 Solving 1 + l = 8.062257748 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 = 8.062257748 + -1 Combine like terms: 1 + -1 = 0 0 + l = 8.062257748 + -1 l = 8.062257748 + -1 Combine like terms: 8.062257748 + -1 = 7.062257748 l = 7.062257748 Simplifying l = 7.062257748Subproblem 2
l + 1 = -8.062257748 Simplifying l + 1 = -8.062257748 Reorder the terms: 1 + l = -8.062257748 Solving 1 + l = -8.062257748 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 = -8.062257748 + -1 Combine like terms: 1 + -1 = 0 0 + l = -8.062257748 + -1 l = -8.062257748 + -1 Combine like terms: -8.062257748 + -1 = -9.062257748 l = -9.062257748 Simplifying l = -9.062257748Solution
The solution to the problem is based on the solutions from the subproblems. l = {7.062257748, -9.062257748}
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