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Simplifying 14f3 + 42f5 + -77f7 = 0 Solving 14f3 + 42f5 + -77f7 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '7f3'. 7f3(2 + 6f2 + -11f4) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'f3' equal to zero and attempt to solve: Simplifying f3 = 0 Solving f3 = 0 Move all terms containing f to the left, all other terms to the right. Simplifying f3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2 + 6f2 + -11f4)' equal to zero and attempt to solve: Simplifying 2 + 6f2 + -11f4 = 0 Solving 2 + 6f2 + -11f4 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -0.1818181818 + -0.5454545455f2 + f4 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + -0.5454545455f2 + 0.1818181818 + f4 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + -0.5454545455f2 + f4 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + -0.5454545455f2 + f4 = 0 + 0.1818181818 -0.5454545455f2 + f4 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 -0.5454545455f2 + f4 = 0.1818181818 The f term is -0.5454545455f2. Take half its coefficient (-0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. -0.5454545455f2 + 0.07438016533 + f4 = 0.1818181818 + 0.07438016533 Reorder the terms: 0.07438016533 + -0.5454545455f2 + f4 = 0.1818181818 + 0.07438016533 Combine like terms: 0.1818181818 + 0.07438016533 = 0.25619834713 0.07438016533 + -0.5454545455f2 + f4 = 0.25619834713 Factor a perfect square on the left side: (f2 + -0.2727272728)(f2 + -0.2727272728) = 0.25619834713 Calculate the square root of the right side: 0.506160397 Break this problem into two subproblems by setting (f2 + -0.2727272728) equal to 0.506160397 and -0.506160397.Subproblem 1
f2 + -0.2727272728 = 0.506160397 Simplifying f2 + -0.2727272728 = 0.506160397 Reorder the terms: -0.2727272728 + f2 = 0.506160397 Solving -0.2727272728 + f2 = 0.506160397 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + f2 = 0.506160397 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + f2 = 0.506160397 + 0.2727272728 f2 = 0.506160397 + 0.2727272728 Combine like terms: 0.506160397 + 0.2727272728 = 0.7788876698 f2 = 0.7788876698 Simplifying f2 = 0.7788876698 Take the square root of each side: f = {-0.882546129, 0.882546129}Subproblem 2
f2 + -0.2727272728 = -0.506160397 Simplifying f2 + -0.2727272728 = -0.506160397 Reorder the terms: -0.2727272728 + f2 = -0.506160397 Solving -0.2727272728 + f2 = -0.506160397 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + f2 = -0.506160397 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + f2 = -0.506160397 + 0.2727272728 f2 = -0.506160397 + 0.2727272728 Combine like terms: -0.506160397 + 0.2727272728 = -0.2334331242 f2 = -0.2334331242 Simplifying f2 = -0.2334331242 Reorder the terms: 0.2334331242 + f2 = -0.2334331242 + 0.2334331242 Combine like terms: -0.2334331242 + 0.2334331242 = 0.0000000000 0.2334331242 + f2 = 0.0000000000 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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