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Simplifying f2 + 9f + -4 = 0 Reorder the terms: -4 + 9f + f2 = 0 Solving -4 + 9f + 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 + 9f + 4 + f2 = 0 + 4 Reorder the terms: -4 + 4 + 9f + f2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 9f + f2 = 0 + 4 9f + f2 = 0 + 4 Combine like terms: 0 + 4 = 4 9f + f2 = 4 The f term is 9f. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9f + 20.25 + f2 = 4 + 20.25 Reorder the terms: 20.25 + 9f + f2 = 4 + 20.25 Combine like terms: 4 + 20.25 = 24.25 20.25 + 9f + f2 = 24.25 Factor a perfect square on the left side: (f + 4.5)(f + 4.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (f + 4.5) equal to 4.924428901 and -4.924428901.Subproblem 1
f + 4.5 = 4.924428901 Simplifying f + 4.5 = 4.924428901 Reorder the terms: 4.5 + f = 4.924428901 Solving 4.5 + f = 4.924428901 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + f = 4.924428901 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + f = 4.924428901 + -4.5 f = 4.924428901 + -4.5 Combine like terms: 4.924428901 + -4.5 = 0.424428901 f = 0.424428901 Simplifying f = 0.424428901Subproblem 2
f + 4.5 = -4.924428901 Simplifying f + 4.5 = -4.924428901 Reorder the terms: 4.5 + f = -4.924428901 Solving 4.5 + f = -4.924428901 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + f = -4.924428901 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + f = -4.924428901 + -4.5 f = -4.924428901 + -4.5 Combine like terms: -4.924428901 + -4.5 = -9.424428901 f = -9.424428901 Simplifying f = -9.424428901Solution
The solution to the problem is based on the solutions from the subproblems. f = {0.424428901, -9.424428901}
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