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Simplifying 0 = l2 + 25l + -540 Reorder the terms: 0 = -540 + 25l + l2 Solving 0 = -540 + 25l + l2 Solving for variable 'l'. Combine like terms: 0 + 540 = 540 540 + -25l + -1l2 = -540 + 25l + l2 + 540 + -25l + -1l2 Reorder the terms: 540 + -25l + -1l2 = -540 + 540 + 25l + -25l + l2 + -1l2 Combine like terms: -540 + 540 = 0 540 + -25l + -1l2 = 0 + 25l + -25l + l2 + -1l2 540 + -25l + -1l2 = 25l + -25l + l2 + -1l2 Combine like terms: 25l + -25l = 0 540 + -25l + -1l2 = 0 + l2 + -1l2 540 + -25l + -1l2 = l2 + -1l2 Combine like terms: l2 + -1l2 = 0 540 + -25l + -1l2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -540 + 25l + l2 = 0 Move the constant term to the right: Add '540' to each side of the equation. -540 + 25l + 540 + l2 = 0 + 540 Reorder the terms: -540 + 540 + 25l + l2 = 0 + 540 Combine like terms: -540 + 540 = 0 0 + 25l + l2 = 0 + 540 25l + l2 = 0 + 540 Combine like terms: 0 + 540 = 540 25l + l2 = 540 The l term is 25l. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25l + 156.25 + l2 = 540 + 156.25 Reorder the terms: 156.25 + 25l + l2 = 540 + 156.25 Combine like terms: 540 + 156.25 = 696.25 156.25 + 25l + l2 = 696.25 Factor a perfect square on the left side: (l + 12.5)(l + 12.5) = 696.25 Calculate the square root of the right side: 26.386549604 Break this problem into two subproblems by setting (l + 12.5) equal to 26.386549604 and -26.386549604.Subproblem 1
l + 12.5 = 26.386549604 Simplifying l + 12.5 = 26.386549604 Reorder the terms: 12.5 + l = 26.386549604 Solving 12.5 + l = 26.386549604 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + l = 26.386549604 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + l = 26.386549604 + -12.5 l = 26.386549604 + -12.5 Combine like terms: 26.386549604 + -12.5 = 13.886549604 l = 13.886549604 Simplifying l = 13.886549604Subproblem 2
l + 12.5 = -26.386549604 Simplifying l + 12.5 = -26.386549604 Reorder the terms: 12.5 + l = -26.386549604 Solving 12.5 + l = -26.386549604 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + l = -26.386549604 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + l = -26.386549604 + -12.5 l = -26.386549604 + -12.5 Combine like terms: -26.386549604 + -12.5 = -38.886549604 l = -38.886549604 Simplifying l = -38.886549604Solution
The solution to the problem is based on the solutions from the subproblems. l = {13.886549604, -38.886549604}
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