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Simplifying f2 + -6f + 4 = 0 Reorder the terms: 4 + -6f + f2 = 0 Solving 4 + -6f + f2 = 0 Solving for variable 'f'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -6f + -4 + f2 = 0 + -4 Reorder the terms: 4 + -4 + -6f + f2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -6f + f2 = 0 + -4 -6f + f2 = 0 + -4 Combine like terms: 0 + -4 = -4 -6f + f2 = -4 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 = -4 + 9 Reorder the terms: 9 + -6f + f2 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + -6f + f2 = 5 Factor a perfect square on the left side: (f + -3)(f + -3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (f + -3) equal to 2.236067978 and -2.236067978.Subproblem 1
f + -3 = 2.236067978 Simplifying f + -3 = 2.236067978 Reorder the terms: -3 + f = 2.236067978 Solving -3 + f = 2.236067978 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 = 2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + f = 2.236067978 + 3 f = 2.236067978 + 3 Combine like terms: 2.236067978 + 3 = 5.236067978 f = 5.236067978 Simplifying f = 5.236067978Subproblem 2
f + -3 = -2.236067978 Simplifying f + -3 = -2.236067978 Reorder the terms: -3 + f = -2.236067978 Solving -3 + f = -2.236067978 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 = -2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + f = -2.236067978 + 3 f = -2.236067978 + 3 Combine like terms: -2.236067978 + 3 = 0.763932022 f = 0.763932022 Simplifying f = 0.763932022Solution
The solution to the problem is based on the solutions from the subproblems. f = {5.236067978, 0.763932022}
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