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Simplifying f2 + -16f = 9 Reorder the terms: -16f + f2 = 9 Solving -16f + f2 = 9 Solving for variable 'f'. Reorder the terms: -9 + -16f + f2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -16f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -16f + 9 + f2 = 0 + 9 Reorder the terms: -9 + 9 + -16f + f2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -16f + f2 = 0 + 9 -16f + f2 = 0 + 9 Combine like terms: 0 + 9 = 9 -16f + f2 = 9 The f term is -16f. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16f + 64 + f2 = 9 + 64 Reorder the terms: 64 + -16f + f2 = 9 + 64 Combine like terms: 9 + 64 = 73 64 + -16f + f2 = 73 Factor a perfect square on the left side: (f + -8)(f + -8) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (f + -8) equal to 8.544003745 and -8.544003745.Subproblem 1
f + -8 = 8.544003745 Simplifying f + -8 = 8.544003745 Reorder the terms: -8 + f = 8.544003745 Solving -8 + f = 8.544003745 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + f = 8.544003745 + 8 Combine like terms: -8 + 8 = 0 0 + f = 8.544003745 + 8 f = 8.544003745 + 8 Combine like terms: 8.544003745 + 8 = 16.544003745 f = 16.544003745 Simplifying f = 16.544003745Subproblem 2
f + -8 = -8.544003745 Simplifying f + -8 = -8.544003745 Reorder the terms: -8 + f = -8.544003745 Solving -8 + f = -8.544003745 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + f = -8.544003745 + 8 Combine like terms: -8 + 8 = 0 0 + f = -8.544003745 + 8 f = -8.544003745 + 8 Combine like terms: -8.544003745 + 8 = -0.544003745 f = -0.544003745 Simplifying f = -0.544003745Solution
The solution to the problem is based on the solutions from the subproblems. f = {16.544003745, -0.544003745}
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