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Simplifying f2 + 10f = 29 Reorder the terms: 10f + f2 = 29 Solving 10f + f2 = 29 Solving for variable 'f'. Reorder the terms: -29 + 10f + f2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + 10f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 10f + 29 + f2 = 0 + 29 Reorder the terms: -29 + 29 + 10f + f2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 10f + f2 = 0 + 29 10f + f2 = 0 + 29 Combine like terms: 0 + 29 = 29 10f + f2 = 29 The f term is 10f. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10f + 25 + f2 = 29 + 25 Reorder the terms: 25 + 10f + f2 = 29 + 25 Combine like terms: 29 + 25 = 54 25 + 10f + f2 = 54 Factor a perfect square on the left side: (f + 5)(f + 5) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (f + 5) equal to 7.348469228 and -7.348469228.Subproblem 1
f + 5 = 7.348469228 Simplifying f + 5 = 7.348469228 Reorder the terms: 5 + f = 7.348469228 Solving 5 + f = 7.348469228 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + f = 7.348469228 + -5 Combine like terms: 5 + -5 = 0 0 + f = 7.348469228 + -5 f = 7.348469228 + -5 Combine like terms: 7.348469228 + -5 = 2.348469228 f = 2.348469228 Simplifying f = 2.348469228Subproblem 2
f + 5 = -7.348469228 Simplifying f + 5 = -7.348469228 Reorder the terms: 5 + f = -7.348469228 Solving 5 + f = -7.348469228 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + f = -7.348469228 + -5 Combine like terms: 5 + -5 = 0 0 + f = -7.348469228 + -5 f = -7.348469228 + -5 Combine like terms: -7.348469228 + -5 = -12.348469228 f = -12.348469228 Simplifying f = -12.348469228Solution
The solution to the problem is based on the solutions from the subproblems. f = {2.348469228, -12.348469228}
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