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Simplifying f2 + 19f + -48 = 0 Reorder the terms: -48 + 19f + f2 = 0 Solving -48 + 19f + f2 = 0 Solving for variable 'f'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 19f + 48 + f2 = 0 + 48 Reorder the terms: -48 + 48 + 19f + f2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 19f + f2 = 0 + 48 19f + f2 = 0 + 48 Combine like terms: 0 + 48 = 48 19f + f2 = 48 The f term is 19f. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19f + 90.25 + f2 = 48 + 90.25 Reorder the terms: 90.25 + 19f + f2 = 48 + 90.25 Combine like terms: 48 + 90.25 = 138.25 90.25 + 19f + f2 = 138.25 Factor a perfect square on the left side: (f + 9.5)(f + 9.5) = 138.25 Calculate the square root of the right side: 11.757976016 Break this problem into two subproblems by setting (f + 9.5) equal to 11.757976016 and -11.757976016.Subproblem 1
f + 9.5 = 11.757976016 Simplifying f + 9.5 = 11.757976016 Reorder the terms: 9.5 + f = 11.757976016 Solving 9.5 + f = 11.757976016 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + f = 11.757976016 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + f = 11.757976016 + -9.5 f = 11.757976016 + -9.5 Combine like terms: 11.757976016 + -9.5 = 2.257976016 f = 2.257976016 Simplifying f = 2.257976016Subproblem 2
f + 9.5 = -11.757976016 Simplifying f + 9.5 = -11.757976016 Reorder the terms: 9.5 + f = -11.757976016 Solving 9.5 + f = -11.757976016 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + f = -11.757976016 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + f = -11.757976016 + -9.5 f = -11.757976016 + -9.5 Combine like terms: -11.757976016 + -9.5 = -21.257976016 f = -21.257976016 Simplifying f = -21.257976016Solution
The solution to the problem is based on the solutions from the subproblems. f = {2.257976016, -21.257976016}
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