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Simplifying f2 + -18f = 1 Reorder the terms: -18f + f2 = 1 Solving -18f + f2 = 1 Solving for variable 'f'. Reorder the terms: -1 + -18f + f2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -18f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -18f + 1 + f2 = 0 + 1 Reorder the terms: -1 + 1 + -18f + f2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -18f + f2 = 0 + 1 -18f + f2 = 0 + 1 Combine like terms: 0 + 1 = 1 -18f + f2 = 1 The f term is -18f. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18f + 81 + f2 = 1 + 81 Reorder the terms: 81 + -18f + f2 = 1 + 81 Combine like terms: 1 + 81 = 82 81 + -18f + f2 = 82 Factor a perfect square on the left side: (f + -9)(f + -9) = 82 Calculate the square root of the right side: 9.055385138 Break this problem into two subproblems by setting (f + -9) equal to 9.055385138 and -9.055385138.Subproblem 1
f + -9 = 9.055385138 Simplifying f + -9 = 9.055385138 Reorder the terms: -9 + f = 9.055385138 Solving -9 + f = 9.055385138 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + f = 9.055385138 + 9 Combine like terms: -9 + 9 = 0 0 + f = 9.055385138 + 9 f = 9.055385138 + 9 Combine like terms: 9.055385138 + 9 = 18.055385138 f = 18.055385138 Simplifying f = 18.055385138Subproblem 2
f + -9 = -9.055385138 Simplifying f + -9 = -9.055385138 Reorder the terms: -9 + f = -9.055385138 Solving -9 + f = -9.055385138 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + f = -9.055385138 + 9 Combine like terms: -9 + 9 = 0 0 + f = -9.055385138 + 9 f = -9.055385138 + 9 Combine like terms: -9.055385138 + 9 = -0.055385138 f = -0.055385138 Simplifying f = -0.055385138Solution
The solution to the problem is based on the solutions from the subproblems. f = {18.055385138, -0.055385138}
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