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Simplifying f(f + 2) = 46 Reorder the terms: f(2 + f) = 46 (2 * f + f * f) = 46 (2f + f2) = 46 Solving 2f + f2 = 46 Solving for variable 'f'. Reorder the terms: -46 + 2f + f2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + 2f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + 2f + 46 + f2 = 0 + 46 Reorder the terms: -46 + 46 + 2f + f2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 2f + f2 = 0 + 46 2f + f2 = 0 + 46 Combine like terms: 0 + 46 = 46 2f + f2 = 46 The f term is 2f. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2f + 1 + f2 = 46 + 1 Reorder the terms: 1 + 2f + f2 = 46 + 1 Combine like terms: 46 + 1 = 47 1 + 2f + f2 = 47 Factor a perfect square on the left side: (f + 1)(f + 1) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (f + 1) equal to 6.8556546 and -6.8556546.Subproblem 1
f + 1 = 6.8556546 Simplifying f + 1 = 6.8556546 Reorder the terms: 1 + f = 6.8556546 Solving 1 + f = 6.8556546 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + f = 6.8556546 + -1 Combine like terms: 1 + -1 = 0 0 + f = 6.8556546 + -1 f = 6.8556546 + -1 Combine like terms: 6.8556546 + -1 = 5.8556546 f = 5.8556546 Simplifying f = 5.8556546Subproblem 2
f + 1 = -6.8556546 Simplifying f + 1 = -6.8556546 Reorder the terms: 1 + f = -6.8556546 Solving 1 + f = -6.8556546 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + f = -6.8556546 + -1 Combine like terms: 1 + -1 = 0 0 + f = -6.8556546 + -1 f = -6.8556546 + -1 Combine like terms: -6.8556546 + -1 = -7.8556546 f = -7.8556546 Simplifying f = -7.8556546Solution
The solution to the problem is based on the solutions from the subproblems. f = {5.8556546, -7.8556546}
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