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Simplifying 35L2 + -5150L + -1112400 = 0 Reorder the terms: -1112400 + -5150L + 35L2 = 0 Solving -1112400 + -5150L + 35L2 = 0 Solving for variable 'L'. Factor out the Greatest Common Factor (GCF), '5'. 5(-222480 + -1030L + 7L2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-222480 + -1030L + 7L2)' equal to zero and attempt to solve: Simplifying -222480 + -1030L + 7L2 = 0 Solving -222480 + -1030L + 7L2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -31782.85714 + -147.1428571L + L2 = 0 Move the constant term to the right: Add '31782.85714' to each side of the equation. -31782.85714 + -147.1428571L + 31782.85714 + L2 = 0 + 31782.85714 Reorder the terms: -31782.85714 + 31782.85714 + -147.1428571L + L2 = 0 + 31782.85714 Combine like terms: -31782.85714 + 31782.85714 = 0.00000 0.00000 + -147.1428571L + L2 = 0 + 31782.85714 -147.1428571L + L2 = 0 + 31782.85714 Combine like terms: 0 + 31782.85714 = 31782.85714 -147.1428571L + L2 = 31782.85714 The L term is -147.1428571L. Take half its coefficient (-73.57142855). Square it (5412.755099) and add it to both sides. Add '5412.755099' to each side of the equation. -147.1428571L + 5412.755099 + L2 = 31782.85714 + 5412.755099 Reorder the terms: 5412.755099 + -147.1428571L + L2 = 31782.85714 + 5412.755099 Combine like terms: 31782.85714 + 5412.755099 = 37195.612239 5412.755099 + -147.1428571L + L2 = 37195.612239 Factor a perfect square on the left side: (L + -73.57142855)(L + -73.57142855) = 37195.612239 Calculate the square root of the right side: 192.861640144 Break this problem into two subproblems by setting (L + -73.57142855) equal to 192.861640144 and -192.861640144.Subproblem 1
L + -73.57142855 = 192.861640144 Simplifying L + -73.57142855 = 192.861640144 Reorder the terms: -73.57142855 + L = 192.861640144 Solving -73.57142855 + L = 192.861640144 Solving for variable 'L'. Move all terms containing L to the left, all other terms to the right. Add '73.57142855' to each side of the equation. -73.57142855 + 73.57142855 + L = 192.861640144 + 73.57142855 Combine like terms: -73.57142855 + 73.57142855 = 0.00000000 0.00000000 + L = 192.861640144 + 73.57142855 L = 192.861640144 + 73.57142855 Combine like terms: 192.861640144 + 73.57142855 = 266.433068694 L = 266.433068694 Simplifying L = 266.433068694Subproblem 2
L + -73.57142855 = -192.861640144 Simplifying L + -73.57142855 = -192.861640144 Reorder the terms: -73.57142855 + L = -192.861640144 Solving -73.57142855 + L = -192.861640144 Solving for variable 'L'. Move all terms containing L to the left, all other terms to the right. Add '73.57142855' to each side of the equation. -73.57142855 + 73.57142855 + L = -192.861640144 + 73.57142855 Combine like terms: -73.57142855 + 73.57142855 = 0.00000000 0.00000000 + L = -192.861640144 + 73.57142855 L = -192.861640144 + 73.57142855 Combine like terms: -192.861640144 + 73.57142855 = -119.290211594 L = -119.290211594 Simplifying L = -119.290211594Solution
The solution to the problem is based on the solutions from the subproblems. L = {266.433068694, -119.290211594}Solution
L = {266.433068694, -119.290211594}
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