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Simplifying 50 = l2 + -3l Reorder the terms: 50 = -3l + l2 Solving 50 = -3l + l2 Solving for variable 'l'. Reorder the terms: 50 + 3l + -1l2 = -3l + 3l + l2 + -1l2 Combine like terms: -3l + 3l = 0 50 + 3l + -1l2 = 0 + l2 + -1l2 50 + 3l + -1l2 = l2 + -1l2 Combine like terms: l2 + -1l2 = 0 50 + 3l + -1l2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -50 + -3l + l2 = 0 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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