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Simplifying 50 + 12L + -1.5L2 = 0 Solving 50 + 12L + -1.5L2 = 0 Solving for variable 'L'. Begin completing the square. Divide all terms by -1.5 the coefficient of the squared term: Divide each side by '-1.5'. -33.33333333 + -8L + L2 = 0 Move the constant term to the right: Add '33.33333333' to each side of the equation. -33.33333333 + -8L + 33.33333333 + L2 = 0 + 33.33333333 Reorder the terms: -33.33333333 + 33.33333333 + -8L + L2 = 0 + 33.33333333 Combine like terms: -33.33333333 + 33.33333333 = 0.00000000 0.00000000 + -8L + L2 = 0 + 33.33333333 -8L + L2 = 0 + 33.33333333 Combine like terms: 0 + 33.33333333 = 33.33333333 -8L + L2 = 33.33333333 The L term is -8L. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8L + 16 + L2 = 33.33333333 + 16 Reorder the terms: 16 + -8L + L2 = 33.33333333 + 16 Combine like terms: 33.33333333 + 16 = 49.33333333 16 + -8L + L2 = 49.33333333 Factor a perfect square on the left side: (L + -4)(L + -4) = 49.33333333 Calculate the square root of the right side: 7.023769168 Break this problem into two subproblems by setting (L + -4) equal to 7.023769168 and -7.023769168.Subproblem 1
L + -4 = 7.023769168 Simplifying L + -4 = 7.023769168 Reorder the terms: -4 + L = 7.023769168 Solving -4 + L = 7.023769168 Solving for variable 'L'. Move all terms containing L to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + L = 7.023769168 + 4 Combine like terms: -4 + 4 = 0 0 + L = 7.023769168 + 4 L = 7.023769168 + 4 Combine like terms: 7.023769168 + 4 = 11.023769168 L = 11.023769168 Simplifying L = 11.023769168Subproblem 2
L + -4 = -7.023769168 Simplifying L + -4 = -7.023769168 Reorder the terms: -4 + L = -7.023769168 Solving -4 + L = -7.023769168 Solving for variable 'L'. Move all terms containing L to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + L = -7.023769168 + 4 Combine like terms: -4 + 4 = 0 0 + L = -7.023769168 + 4 L = -7.023769168 + 4 Combine like terms: -7.023769168 + 4 = -3.023769168 L = -3.023769168 Simplifying L = -3.023769168Solution
The solution to the problem is based on the solutions from the subproblems. L = {11.023769168, -3.023769168}
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