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Simplifying (L + -3) * L = 50 Reorder the terms: (-3 + L) * L = 50 Reorder the terms for easier multiplication: L(-3 + L) = 50 (-3 * L + L * L) = 50 (-3L + L2) = 50 Solving -3L + L2 = 50 Solving for variable 'L'. Reorder the terms: -50 + -3L + L2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + -3L + L2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -3L + 50 + L2 = 0 + 50 Reorder the terms: -50 + 50 + -3L + L2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -3L + L2 = 0 + 50 -3L + L2 = 0 + 50 Combine like terms: 0 + 50 = 50 -3L + L2 = 50 The L term is -3L. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3L + 2.25 + L2 = 50 + 2.25 Reorder the terms: 2.25 + -3L + L2 = 50 + 2.25 Combine like terms: 50 + 2.25 = 52.25 2.25 + -3L + L2 = 52.25 Factor a perfect square on the left side: (L + -1.5)(L + -1.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (L + -1.5) equal to 7.228416147 and -7.228416147.Subproblem 1
L + -1.5 = 7.228416147 Simplifying L + -1.5 = 7.228416147 Reorder the terms: -1.5 + L = 7.228416147 Solving -1.5 + L = 7.228416147 Solving for variable 'L'. Move all terms containing L to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + L = 7.228416147 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + L = 7.228416147 + 1.5 L = 7.228416147 + 1.5 Combine like terms: 7.228416147 + 1.5 = 8.728416147 L = 8.728416147 Simplifying L = 8.728416147Subproblem 2
L + -1.5 = -7.228416147 Simplifying L + -1.5 = -7.228416147 Reorder the terms: -1.5 + L = -7.228416147 Solving -1.5 + L = -7.228416147 Solving for variable 'L'. Move all terms containing L to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + L = -7.228416147 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + L = -7.228416147 + 1.5 L = -7.228416147 + 1.5 Combine like terms: -7.228416147 + 1.5 = -5.728416147 L = -5.728416147 Simplifying L = -5.728416147Solution
The solution to the problem is based on the solutions from the subproblems. L = {8.728416147, -5.728416147}
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