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Simplifying 7l2 + -274l + -440 = 0 Reorder the terms: -440 + -274l + 7l2 = 0 Solving -440 + -274l + 7l2 = 0 Solving for variable 'l'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -62.85714286 + -39.14285714l + l2 = 0 Move the constant term to the right: Add '62.85714286' to each side of the equation. -62.85714286 + -39.14285714l + 62.85714286 + l2 = 0 + 62.85714286 Reorder the terms: -62.85714286 + 62.85714286 + -39.14285714l + l2 = 0 + 62.85714286 Combine like terms: -62.85714286 + 62.85714286 = 0.00000000 0.00000000 + -39.14285714l + l2 = 0 + 62.85714286 -39.14285714l + l2 = 0 + 62.85714286 Combine like terms: 0 + 62.85714286 = 62.85714286 -39.14285714l + l2 = 62.85714286 The l term is -39.14285714l. Take half its coefficient (-19.57142857). Square it (383.0408163) and add it to both sides. Add '383.0408163' to each side of the equation. -39.14285714l + 383.0408163 + l2 = 62.85714286 + 383.0408163 Reorder the terms: 383.0408163 + -39.14285714l + l2 = 62.85714286 + 383.0408163 Combine like terms: 62.85714286 + 383.0408163 = 445.89795916 383.0408163 + -39.14285714l + l2 = 445.89795916 Factor a perfect square on the left side: (l + -19.57142857)(l + -19.57142857) = 445.89795916 Calculate the square root of the right side: 21.116296057 Break this problem into two subproblems by setting (l + -19.57142857) equal to 21.116296057 and -21.116296057.Subproblem 1
l + -19.57142857 = 21.116296057 Simplifying l + -19.57142857 = 21.116296057 Reorder the terms: -19.57142857 + l = 21.116296057 Solving -19.57142857 + l = 21.116296057 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '19.57142857' to each side of the equation. -19.57142857 + 19.57142857 + l = 21.116296057 + 19.57142857 Combine like terms: -19.57142857 + 19.57142857 = 0.00000000 0.00000000 + l = 21.116296057 + 19.57142857 l = 21.116296057 + 19.57142857 Combine like terms: 21.116296057 + 19.57142857 = 40.687724627 l = 40.687724627 Simplifying l = 40.687724627Subproblem 2
l + -19.57142857 = -21.116296057 Simplifying l + -19.57142857 = -21.116296057 Reorder the terms: -19.57142857 + l = -21.116296057 Solving -19.57142857 + l = -21.116296057 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '19.57142857' to each side of the equation. -19.57142857 + 19.57142857 + l = -21.116296057 + 19.57142857 Combine like terms: -19.57142857 + 19.57142857 = 0.00000000 0.00000000 + l = -21.116296057 + 19.57142857 l = -21.116296057 + 19.57142857 Combine like terms: -21.116296057 + 19.57142857 = -1.544867487 l = -1.544867487 Simplifying l = -1.544867487Solution
The solution to the problem is based on the solutions from the subproblems. l = {40.687724627, -1.544867487}
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