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Simplifying 30 = l(l + 4) Reorder the terms: 30 = l(4 + l) 30 = (4 * l + l * l) 30 = (4l + l2) Solving 30 = 4l + l2 Solving for variable 'l'. Reorder the terms: 30 + -4l + -1l2 = 4l + -4l + l2 + -1l2 Combine like terms: 4l + -4l = 0 30 + -4l + -1l2 = 0 + l2 + -1l2 30 + -4l + -1l2 = l2 + -1l2 Combine like terms: l2 + -1l2 = 0 30 + -4l + -1l2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + 4l + l2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 4l + 30 + l2 = 0 + 30 Reorder the terms: -30 + 30 + 4l + l2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 4l + l2 = 0 + 30 4l + l2 = 0 + 30 Combine like terms: 0 + 30 = 30 4l + l2 = 30 The l term is 4l. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4l + 4 + l2 = 30 + 4 Reorder the terms: 4 + 4l + l2 = 30 + 4 Combine like terms: 30 + 4 = 34 4 + 4l + l2 = 34 Factor a perfect square on the left side: (l + 2)(l + 2) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (l + 2) equal to 5.830951895 and -5.830951895.Subproblem 1
l + 2 = 5.830951895 Simplifying l + 2 = 5.830951895 Reorder the terms: 2 + l = 5.830951895 Solving 2 + l = 5.830951895 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + l = 5.830951895 + -2 Combine like terms: 2 + -2 = 0 0 + l = 5.830951895 + -2 l = 5.830951895 + -2 Combine like terms: 5.830951895 + -2 = 3.830951895 l = 3.830951895 Simplifying l = 3.830951895Subproblem 2
l + 2 = -5.830951895 Simplifying l + 2 = -5.830951895 Reorder the terms: 2 + l = -5.830951895 Solving 2 + l = -5.830951895 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + l = -5.830951895 + -2 Combine like terms: 2 + -2 = 0 0 + l = -5.830951895 + -2 l = -5.830951895 + -2 Combine like terms: -5.830951895 + -2 = -7.830951895 l = -7.830951895 Simplifying l = -7.830951895Solution
The solution to the problem is based on the solutions from the subproblems. l = {3.830951895, -7.830951895}
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