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Simplifying f2 + -8f + -11 = 0 Reorder the terms: -11 + -8f + f2 = 0 Solving -11 + -8f + f2 = 0 Solving for variable 'f'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -8f + 11 + f2 = 0 + 11 Reorder the terms: -11 + 11 + -8f + f2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -8f + f2 = 0 + 11 -8f + f2 = 0 + 11 Combine like terms: 0 + 11 = 11 -8f + f2 = 11 The f term is -8f. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8f + 16 + f2 = 11 + 16 Reorder the terms: 16 + -8f + f2 = 11 + 16 Combine like terms: 11 + 16 = 27 16 + -8f + f2 = 27 Factor a perfect square on the left side: (f + -4)(f + -4) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (f + -4) equal to 5.196152423 and -5.196152423.Subproblem 1
f + -4 = 5.196152423 Simplifying f + -4 = 5.196152423 Reorder the terms: -4 + f = 5.196152423 Solving -4 + f = 5.196152423 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + f = 5.196152423 + 4 Combine like terms: -4 + 4 = 0 0 + f = 5.196152423 + 4 f = 5.196152423 + 4 Combine like terms: 5.196152423 + 4 = 9.196152423 f = 9.196152423 Simplifying f = 9.196152423Subproblem 2
f + -4 = -5.196152423 Simplifying f + -4 = -5.196152423 Reorder the terms: -4 + f = -5.196152423 Solving -4 + f = -5.196152423 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + f = -5.196152423 + 4 Combine like terms: -4 + 4 = 0 0 + f = -5.196152423 + 4 f = -5.196152423 + 4 Combine like terms: -5.196152423 + 4 = -1.196152423 f = -1.196152423 Simplifying f = -1.196152423Solution
The solution to the problem is based on the solutions from the subproblems. f = {9.196152423, -1.196152423}
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