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Simplifying f2 + 6f = 37 Reorder the terms: 6f + f2 = 37 Solving 6f + f2 = 37 Solving for variable 'f'. Reorder the terms: -37 + 6f + f2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + 6f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + 6f + 37 + f2 = 0 + 37 Reorder the terms: -37 + 37 + 6f + f2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 6f + f2 = 0 + 37 6f + f2 = 0 + 37 Combine like terms: 0 + 37 = 37 6f + f2 = 37 The f term is 6f. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6f + 9 + f2 = 37 + 9 Reorder the terms: 9 + 6f + f2 = 37 + 9 Combine like terms: 37 + 9 = 46 9 + 6f + f2 = 46 Factor a perfect square on the left side: (f + 3)(f + 3) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (f + 3) equal to 6.782329983 and -6.782329983.Subproblem 1
f + 3 = 6.782329983 Simplifying f + 3 = 6.782329983 Reorder the terms: 3 + f = 6.782329983 Solving 3 + f = 6.782329983 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + f = 6.782329983 + -3 Combine like terms: 3 + -3 = 0 0 + f = 6.782329983 + -3 f = 6.782329983 + -3 Combine like terms: 6.782329983 + -3 = 3.782329983 f = 3.782329983 Simplifying f = 3.782329983Subproblem 2
f + 3 = -6.782329983 Simplifying f + 3 = -6.782329983 Reorder the terms: 3 + f = -6.782329983 Solving 3 + f = -6.782329983 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + f = -6.782329983 + -3 Combine like terms: 3 + -3 = 0 0 + f = -6.782329983 + -3 f = -6.782329983 + -3 Combine like terms: -6.782329983 + -3 = -9.782329983 f = -9.782329983 Simplifying f = -9.782329983Solution
The solution to the problem is based on the solutions from the subproblems. f = {3.782329983, -9.782329983}
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