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Simplifying 94 = l(l + -4) Reorder the terms: 94 = l(-4 + l) 94 = (-4 * l + l * l) 94 = (-4l + l2) Solving 94 = -4l + l2 Solving for variable 'l'. Reorder the terms: 94 + 4l + -1l2 = -4l + 4l + l2 + -1l2 Combine like terms: -4l + 4l = 0 94 + 4l + -1l2 = 0 + l2 + -1l2 94 + 4l + -1l2 = l2 + -1l2 Combine like terms: l2 + -1l2 = 0 94 + 4l + -1l2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -94 + -4l + l2 = 0 Move the constant term to the right: Add '94' to each side of the equation. -94 + -4l + 94 + l2 = 0 + 94 Reorder the terms: -94 + 94 + -4l + l2 = 0 + 94 Combine like terms: -94 + 94 = 0 0 + -4l + l2 = 0 + 94 -4l + l2 = 0 + 94 Combine like terms: 0 + 94 = 94 -4l + l2 = 94 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 = 94 + 4 Reorder the terms: 4 + -4l + l2 = 94 + 4 Combine like terms: 94 + 4 = 98 4 + -4l + l2 = 98 Factor a perfect square on the left side: (l + -2)(l + -2) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (l + -2) equal to 9.899494937 and -9.899494937.Subproblem 1
l + -2 = 9.899494937 Simplifying l + -2 = 9.899494937 Reorder the terms: -2 + l = 9.899494937 Solving -2 + l = 9.899494937 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 = 9.899494937 + 2 Combine like terms: -2 + 2 = 0 0 + l = 9.899494937 + 2 l = 9.899494937 + 2 Combine like terms: 9.899494937 + 2 = 11.899494937 l = 11.899494937 Simplifying l = 11.899494937Subproblem 2
l + -2 = -9.899494937 Simplifying l + -2 = -9.899494937 Reorder the terms: -2 + l = -9.899494937 Solving -2 + l = -9.899494937 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 = -9.899494937 + 2 Combine like terms: -2 + 2 = 0 0 + l = -9.899494937 + 2 l = -9.899494937 + 2 Combine like terms: -9.899494937 + 2 = -7.899494937 l = -7.899494937 Simplifying l = -7.899494937Solution
The solution to the problem is based on the solutions from the subproblems. l = {11.899494937, -7.899494937}
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