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Simplifying 2l2 + -9l + -168 = 0 Reorder the terms: -168 + -9l + 2l2 = 0 Solving -168 + -9l + 2l2 = 0 Solving for variable 'l'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -84 + -4.5l + l2 = 0 Move the constant term to the right: Add '84' to each side of the equation. -84 + -4.5l + 84 + l2 = 0 + 84 Reorder the terms: -84 + 84 + -4.5l + l2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + -4.5l + l2 = 0 + 84 -4.5l + l2 = 0 + 84 Combine like terms: 0 + 84 = 84 -4.5l + l2 = 84 The l term is -4.5l. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5l + 5.0625 + l2 = 84 + 5.0625 Reorder the terms: 5.0625 + -4.5l + l2 = 84 + 5.0625 Combine like terms: 84 + 5.0625 = 89.0625 5.0625 + -4.5l + l2 = 89.0625 Factor a perfect square on the left side: (l + -2.25)(l + -2.25) = 89.0625 Calculate the square root of the right side: 9.437293044 Break this problem into two subproblems by setting (l + -2.25) equal to 9.437293044 and -9.437293044.Subproblem 1
l + -2.25 = 9.437293044 Simplifying l + -2.25 = 9.437293044 Reorder the terms: -2.25 + l = 9.437293044 Solving -2.25 + l = 9.437293044 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + l = 9.437293044 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + l = 9.437293044 + 2.25 l = 9.437293044 + 2.25 Combine like terms: 9.437293044 + 2.25 = 11.687293044 l = 11.687293044 Simplifying l = 11.687293044Subproblem 2
l + -2.25 = -9.437293044 Simplifying l + -2.25 = -9.437293044 Reorder the terms: -2.25 + l = -9.437293044 Solving -2.25 + l = -9.437293044 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + l = -9.437293044 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + l = -9.437293044 + 2.25 l = -9.437293044 + 2.25 Combine like terms: -9.437293044 + 2.25 = -7.187293044 l = -7.187293044 Simplifying l = -7.187293044Solution
The solution to the problem is based on the solutions from the subproblems. l = {11.687293044, -7.187293044}
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