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Simplifying L2 + -9L + 3 = 0 Reorder the terms: 3 + -9L + L2 = 0 Solving 3 + -9L + L2 = 0 Solving for variable 'L'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -9L + -3 + L2 = 0 + -3 Reorder the terms: 3 + -3 + -9L + L2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -9L + L2 = 0 + -3 -9L + L2 = 0 + -3 Combine like terms: 0 + -3 = -3 -9L + L2 = -3 The L term is -9L. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9L + 20.25 + L2 = -3 + 20.25 Reorder the terms: 20.25 + -9L + L2 = -3 + 20.25 Combine like terms: -3 + 20.25 = 17.25 20.25 + -9L + L2 = 17.25 Factor a perfect square on the left side: (L + -4.5)(L + -4.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (L + -4.5) equal to 4.153311931 and -4.153311931.Subproblem 1
L + -4.5 = 4.153311931 Simplifying L + -4.5 = 4.153311931 Reorder the terms: -4.5 + L = 4.153311931 Solving -4.5 + L = 4.153311931 Solving for variable 'L'. Move all terms containing L to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + L = 4.153311931 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + L = 4.153311931 + 4.5 L = 4.153311931 + 4.5 Combine like terms: 4.153311931 + 4.5 = 8.653311931 L = 8.653311931 Simplifying L = 8.653311931Subproblem 2
L + -4.5 = -4.153311931 Simplifying L + -4.5 = -4.153311931 Reorder the terms: -4.5 + L = -4.153311931 Solving -4.5 + L = -4.153311931 Solving for variable 'L'. Move all terms containing L to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + L = -4.153311931 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + L = -4.153311931 + 4.5 L = -4.153311931 + 4.5 Combine like terms: -4.153311931 + 4.5 = 0.346688069 L = 0.346688069 Simplifying L = 0.346688069Solution
The solution to the problem is based on the solutions from the subproblems. L = {8.653311931, 0.346688069}
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