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Simplifying f2 + 28f = 25 Reorder the terms: 28f + f2 = 25 Solving 28f + f2 = 25 Solving for variable 'f'. Reorder the terms: -25 + 28f + f2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 28f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 28f + 25 + f2 = 0 + 25 Reorder the terms: -25 + 25 + 28f + f2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 28f + f2 = 0 + 25 28f + f2 = 0 + 25 Combine like terms: 0 + 25 = 25 28f + f2 = 25 The f term is 28f. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28f + 196 + f2 = 25 + 196 Reorder the terms: 196 + 28f + f2 = 25 + 196 Combine like terms: 25 + 196 = 221 196 + 28f + f2 = 221 Factor a perfect square on the left side: (f + 14)(f + 14) = 221 Calculate the square root of the right side: 14.866068747 Break this problem into two subproblems by setting (f + 14) equal to 14.866068747 and -14.866068747.Subproblem 1
f + 14 = 14.866068747 Simplifying f + 14 = 14.866068747 Reorder the terms: 14 + f = 14.866068747 Solving 14 + f = 14.866068747 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + f = 14.866068747 + -14 Combine like terms: 14 + -14 = 0 0 + f = 14.866068747 + -14 f = 14.866068747 + -14 Combine like terms: 14.866068747 + -14 = 0.866068747 f = 0.866068747 Simplifying f = 0.866068747Subproblem 2
f + 14 = -14.866068747 Simplifying f + 14 = -14.866068747 Reorder the terms: 14 + f = -14.866068747 Solving 14 + f = -14.866068747 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + f = -14.866068747 + -14 Combine like terms: 14 + -14 = 0 0 + f = -14.866068747 + -14 f = -14.866068747 + -14 Combine like terms: -14.866068747 + -14 = -28.866068747 f = -28.866068747 Simplifying f = -28.866068747Solution
The solution to the problem is based on the solutions from the subproblems. f = {0.866068747, -28.866068747}
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