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Simplifying 250 = 10L + -0.1L2 Solving 250 = 10L + -0.1L2 Solving for variable 'L'. Reorder the terms: 250 + -10L + 0.1L2 = 10L + -10L + -0.1L2 + 0.1L2 Combine like terms: 10L + -10L = 0 250 + -10L + 0.1L2 = 0 + -0.1L2 + 0.1L2 250 + -10L + 0.1L2 = -0.1L2 + 0.1L2 Combine like terms: -0.1L2 + 0.1L2 = 0.0 250 + -10L + 0.1L2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 2500 + -100L + L2 = 0 Move the constant term to the right: Add '-2500' to each side of the equation. 2500 + -100L + -2500 + L2 = 0 + -2500 Reorder the terms: 2500 + -2500 + -100L + L2 = 0 + -2500 Combine like terms: 2500 + -2500 = 0 0 + -100L + L2 = 0 + -2500 -100L + L2 = 0 + -2500 Combine like terms: 0 + -2500 = -2500 -100L + L2 = -2500 The L term is -100L. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100L + 2500 + L2 = -2500 + 2500 Reorder the terms: 2500 + -100L + L2 = -2500 + 2500 Combine like terms: -2500 + 2500 = 0 2500 + -100L + L2 = 0 Factor a perfect square on the left side: (L + -50)(L + -50) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (L + -50) equal to 0 and 0.Subproblem 1
L + -50 = 0 Simplifying L + -50 = 0 Reorder the terms: -50 + L = 0 Solving -50 + L = 0 Solving for variable 'L'. Move all terms containing L to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + L = 0 + 50 Combine like terms: -50 + 50 = 0 0 + L = 0 + 50 L = 0 + 50 Combine like terms: 0 + 50 = 50 L = 50 Simplifying L = 50Subproblem 2
L + -50 = 0 Simplifying L + -50 = 0 Reorder the terms: -50 + L = 0 Solving -50 + L = 0 Solving for variable 'L'. Move all terms containing L to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + L = 0 + 50 Combine like terms: -50 + 50 = 0 0 + L = 0 + 50 L = 0 + 50 Combine like terms: 0 + 50 = 50 L = 50 Simplifying L = 50Solution
The solution to the problem is based on the solutions from the subproblems. L = {50, 50}
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