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Simplifying -0.6l2 + 36l = 300 Reorder the terms: 36l + -0.6l2 = 300 Solving 36l + -0.6l2 = 300 Solving for variable 'l'. Reorder the terms: -300 + 36l + -0.6l2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + 36l + -0.6l2 = 0 Begin completing the square. Divide all terms by -0.6 the coefficient of the squared term: Divide each side by '-0.6'. 500 + -60l + l2 = 0 Move the constant term to the right: Add '-500' to each side of the equation. 500 + -60l + -500 + l2 = 0 + -500 Reorder the terms: 500 + -500 + -60l + l2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -60l + l2 = 0 + -500 -60l + l2 = 0 + -500 Combine like terms: 0 + -500 = -500 -60l + l2 = -500 The l term is -60l. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60l + 900 + l2 = -500 + 900 Reorder the terms: 900 + -60l + l2 = -500 + 900 Combine like terms: -500 + 900 = 400 900 + -60l + l2 = 400 Factor a perfect square on the left side: (l + -30)(l + -30) = 400 Calculate the square root of the right side: 20 Break this problem into two subproblems by setting (l + -30) equal to 20 and -20.Subproblem 1
l + -30 = 20 Simplifying l + -30 = 20 Reorder the terms: -30 + l = 20 Solving -30 + l = 20 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + l = 20 + 30 Combine like terms: -30 + 30 = 0 0 + l = 20 + 30 l = 20 + 30 Combine like terms: 20 + 30 = 50 l = 50 Simplifying l = 50Subproblem 2
l + -30 = -20 Simplifying l + -30 = -20 Reorder the terms: -30 + l = -20 Solving -30 + l = -20 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + l = -20 + 30 Combine like terms: -30 + 30 = 0 0 + l = -20 + 30 l = -20 + 30 Combine like terms: -20 + 30 = 10 l = 10 Simplifying l = 10Solution
The solution to the problem is based on the solutions from the subproblems. l = {50, 10}
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