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Simplifying (l + 256) + (l + 4) = l2 Reorder the terms: (256 + l) + (l + 4) = l2 Remove parenthesis around (256 + l) 256 + l + (l + 4) = l2 Reorder the terms: 256 + l + (4 + l) = l2 Remove parenthesis around (4 + l) 256 + l + 4 + l = l2 Reorder the terms: 256 + 4 + l + l = l2 Combine like terms: 256 + 4 = 260 260 + l + l = l2 Combine like terms: l + l = 2l 260 + 2l = l2 Solving 260 + 2l = l2 Solving for variable 'l'. Combine like terms: l2 + -1l2 = 0 260 + 2l + -1l2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -260 + -2l + l2 = 0 Move the constant term to the right: Add '260' to each side of the equation. -260 + -2l + 260 + l2 = 0 + 260 Reorder the terms: -260 + 260 + -2l + l2 = 0 + 260 Combine like terms: -260 + 260 = 0 0 + -2l + l2 = 0 + 260 -2l + l2 = 0 + 260 Combine like terms: 0 + 260 = 260 -2l + l2 = 260 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 = 260 + 1 Reorder the terms: 1 + -2l + l2 = 260 + 1 Combine like terms: 260 + 1 = 261 1 + -2l + l2 = 261 Factor a perfect square on the left side: (l + -1)(l + -1) = 261 Calculate the square root of the right side: 16.155494421 Break this problem into two subproblems by setting (l + -1) equal to 16.155494421 and -16.155494421.Subproblem 1
l + -1 = 16.155494421 Simplifying l + -1 = 16.155494421 Reorder the terms: -1 + l = 16.155494421 Solving -1 + l = 16.155494421 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 = 16.155494421 + 1 Combine like terms: -1 + 1 = 0 0 + l = 16.155494421 + 1 l = 16.155494421 + 1 Combine like terms: 16.155494421 + 1 = 17.155494421 l = 17.155494421 Simplifying l = 17.155494421Subproblem 2
l + -1 = -16.155494421 Simplifying l + -1 = -16.155494421 Reorder the terms: -1 + l = -16.155494421 Solving -1 + l = -16.155494421 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 = -16.155494421 + 1 Combine like terms: -1 + 1 = 0 0 + l = -16.155494421 + 1 l = -16.155494421 + 1 Combine like terms: -16.155494421 + 1 = -15.155494421 l = -15.155494421 Simplifying l = -15.155494421Solution
The solution to the problem is based on the solutions from the subproblems. l = {17.155494421, -15.155494421}
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