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Simplifying f2 = 20f + -16 Reorder the terms: f2 = -16 + 20f Solving f2 = -16 + 20f Solving for variable 'f'. Reorder the terms: 16 + -20f + f2 = -16 + 20f + 16 + -20f Reorder the terms: 16 + -20f + f2 = -16 + 16 + 20f + -20f Combine like terms: -16 + 16 = 0 16 + -20f + f2 = 0 + 20f + -20f 16 + -20f + f2 = 20f + -20f Combine like terms: 20f + -20f = 0 16 + -20f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -20f + -16 + f2 = 0 + -16 Reorder the terms: 16 + -16 + -20f + f2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -20f + f2 = 0 + -16 -20f + f2 = 0 + -16 Combine like terms: 0 + -16 = -16 -20f + f2 = -16 The f term is -20f. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20f + 100 + f2 = -16 + 100 Reorder the terms: 100 + -20f + f2 = -16 + 100 Combine like terms: -16 + 100 = 84 100 + -20f + f2 = 84 Factor a perfect square on the left side: (f + -10)(f + -10) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (f + -10) equal to 9.16515139 and -9.16515139.Subproblem 1
f + -10 = 9.16515139 Simplifying f + -10 = 9.16515139 Reorder the terms: -10 + f = 9.16515139 Solving -10 + f = 9.16515139 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + f = 9.16515139 + 10 Combine like terms: -10 + 10 = 0 0 + f = 9.16515139 + 10 f = 9.16515139 + 10 Combine like terms: 9.16515139 + 10 = 19.16515139 f = 19.16515139 Simplifying f = 19.16515139Subproblem 2
f + -10 = -9.16515139 Simplifying f + -10 = -9.16515139 Reorder the terms: -10 + f = -9.16515139 Solving -10 + f = -9.16515139 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + f = -9.16515139 + 10 Combine like terms: -10 + 10 = 0 0 + f = -9.16515139 + 10 f = -9.16515139 + 10 Combine like terms: -9.16515139 + 10 = 0.83484861 f = 0.83484861 Simplifying f = 0.83484861Solution
The solution to the problem is based on the solutions from the subproblems. f = {19.16515139, 0.83484861}
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