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Simplifying f2 + 8f = 41 Reorder the terms: 8f + f2 = 41 Solving 8f + f2 = 41 Solving for variable 'f'. Reorder the terms: -41 + 8f + f2 = 41 + -41 Combine like terms: 41 + -41 = 0 -41 + 8f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 8f + 41 + f2 = 0 + 41 Reorder the terms: -41 + 41 + 8f + f2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 8f + f2 = 0 + 41 8f + f2 = 0 + 41 Combine like terms: 0 + 41 = 41 8f + f2 = 41 The f term is 8f. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8f + 16 + f2 = 41 + 16 Reorder the terms: 16 + 8f + f2 = 41 + 16 Combine like terms: 41 + 16 = 57 16 + 8f + f2 = 57 Factor a perfect square on the left side: (f + 4)(f + 4) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (f + 4) equal to 7.549834435 and -7.549834435.Subproblem 1
f + 4 = 7.549834435 Simplifying f + 4 = 7.549834435 Reorder the terms: 4 + f = 7.549834435 Solving 4 + f = 7.549834435 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + f = 7.549834435 + -4 Combine like terms: 4 + -4 = 0 0 + f = 7.549834435 + -4 f = 7.549834435 + -4 Combine like terms: 7.549834435 + -4 = 3.549834435 f = 3.549834435 Simplifying f = 3.549834435Subproblem 2
f + 4 = -7.549834435 Simplifying f + 4 = -7.549834435 Reorder the terms: 4 + f = -7.549834435 Solving 4 + f = -7.549834435 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + f = -7.549834435 + -4 Combine like terms: 4 + -4 = 0 0 + f = -7.549834435 + -4 f = -7.549834435 + -4 Combine like terms: -7.549834435 + -4 = -11.549834435 f = -11.549834435 Simplifying f = -11.549834435Solution
The solution to the problem is based on the solutions from the subproblems. f = {3.549834435, -11.549834435}
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