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Simplifying 4L4 + -36L2 + -108 = 0 Reorder the terms: -108 + -36L2 + 4L4 = 0 Solving -108 + -36L2 + 4L4 = 0 Solving for variable 'L'. Factor out the Greatest Common Factor (GCF), '4'. 4(-27 + -9L2 + L4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-27 + -9L2 + L4)' equal to zero and attempt to solve: Simplifying -27 + -9L2 + L4 = 0 Solving -27 + -9L2 + L4 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -9L2 + 27 + L4 = 0 + 27 Reorder the terms: -27 + 27 + -9L2 + L4 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -9L2 + L4 = 0 + 27 -9L2 + L4 = 0 + 27 Combine like terms: 0 + 27 = 27 -9L2 + L4 = 27 The L term is -9L2. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9L2 + 20.25 + L4 = 27 + 20.25 Reorder the terms: 20.25 + -9L2 + L4 = 27 + 20.25 Combine like terms: 27 + 20.25 = 47.25 20.25 + -9L2 + L4 = 47.25 Factor a perfect square on the left side: (L2 + -4.5)(L2 + -4.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (L2 + -4.5) equal to 6.873863542 and -6.873863542.Subproblem 1
L2 + -4.5 = 6.873863542 Simplifying L2 + -4.5 = 6.873863542 Reorder the terms: -4.5 + L2 = 6.873863542 Solving -4.5 + L2 = 6.873863542 Solving for variable 'L'. Move all terms containing L to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + L2 = 6.873863542 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + L2 = 6.873863542 + 4.5 L2 = 6.873863542 + 4.5 Combine like terms: 6.873863542 + 4.5 = 11.373863542 L2 = 11.373863542 Simplifying L2 = 11.373863542 Take the square root of each side: L = {-3.372515907, 3.372515907}Subproblem 2
L2 + -4.5 = -6.873863542 Simplifying L2 + -4.5 = -6.873863542 Reorder the terms: -4.5 + L2 = -6.873863542 Solving -4.5 + L2 = -6.873863542 Solving for variable 'L'. Move all terms containing L to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + L2 = -6.873863542 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + L2 = -6.873863542 + 4.5 L2 = -6.873863542 + 4.5 Combine like terms: -6.873863542 + 4.5 = -2.373863542 L2 = -2.373863542 Simplifying L2 = -2.373863542 Reorder the terms: 2.373863542 + L2 = -2.373863542 + 2.373863542 Combine like terms: -2.373863542 + 2.373863542 = 0.000000000 2.373863542 + L2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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