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Simplifying f2 + -8f + 1 = 0 Reorder the terms: 1 + -8f + f2 = 0 Solving 1 + -8f + f2 = 0 Solving for variable 'f'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -8f + -1 + f2 = 0 + -1 Reorder the terms: 1 + -1 + -8f + f2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8f + f2 = 0 + -1 -8f + f2 = 0 + -1 Combine like terms: 0 + -1 = -1 -8f + f2 = -1 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 = -1 + 16 Reorder the terms: 16 + -8f + f2 = -1 + 16 Combine like terms: -1 + 16 = 15 16 + -8f + f2 = 15 Factor a perfect square on the left side: (f + -4)(f + -4) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (f + -4) equal to 3.872983346 and -3.872983346.Subproblem 1
f + -4 = 3.872983346 Simplifying f + -4 = 3.872983346 Reorder the terms: -4 + f = 3.872983346 Solving -4 + f = 3.872983346 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 = 3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + f = 3.872983346 + 4 f = 3.872983346 + 4 Combine like terms: 3.872983346 + 4 = 7.872983346 f = 7.872983346 Simplifying f = 7.872983346Subproblem 2
f + -4 = -3.872983346 Simplifying f + -4 = -3.872983346 Reorder the terms: -4 + f = -3.872983346 Solving -4 + f = -3.872983346 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 = -3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + f = -3.872983346 + 4 f = -3.872983346 + 4 Combine like terms: -3.872983346 + 4 = 0.127016654 f = 0.127016654 Simplifying f = 0.127016654Solution
The solution to the problem is based on the solutions from the subproblems. f = {7.872983346, 0.127016654}
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