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Simplifying f2 + 18f = 47 Reorder the terms: 18f + f2 = 47 Solving 18f + f2 = 47 Solving for variable 'f'. Reorder the terms: -47 + 18f + f2 = 47 + -47 Combine like terms: 47 + -47 = 0 -47 + 18f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + 18f + 47 + f2 = 0 + 47 Reorder the terms: -47 + 47 + 18f + f2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 18f + f2 = 0 + 47 18f + f2 = 0 + 47 Combine like terms: 0 + 47 = 47 18f + f2 = 47 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 = 47 + 81 Reorder the terms: 81 + 18f + f2 = 47 + 81 Combine like terms: 47 + 81 = 128 81 + 18f + f2 = 128 Factor a perfect square on the left side: (f + 9)(f + 9) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (f + 9) equal to 11.313708499 and -11.313708499.Subproblem 1
f + 9 = 11.313708499 Simplifying f + 9 = 11.313708499 Reorder the terms: 9 + f = 11.313708499 Solving 9 + f = 11.313708499 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 = 11.313708499 + -9 Combine like terms: 9 + -9 = 0 0 + f = 11.313708499 + -9 f = 11.313708499 + -9 Combine like terms: 11.313708499 + -9 = 2.313708499 f = 2.313708499 Simplifying f = 2.313708499Subproblem 2
f + 9 = -11.313708499 Simplifying f + 9 = -11.313708499 Reorder the terms: 9 + f = -11.313708499 Solving 9 + f = -11.313708499 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 = -11.313708499 + -9 Combine like terms: 9 + -9 = 0 0 + f = -11.313708499 + -9 f = -11.313708499 + -9 Combine like terms: -11.313708499 + -9 = -20.313708499 f = -20.313708499 Simplifying f = -20.313708499Solution
The solution to the problem is based on the solutions from the subproblems. f = {2.313708499, -20.313708499}
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