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Simplifying f(f + -3) = f + 10 Reorder the terms: f(-3 + f) = f + 10 (-3 * f + f * f) = f + 10 (-3f + f2) = f + 10 Reorder the terms: -3f + f2 = 10 + f Solving -3f + f2 = 10 + f Solving for variable 'f'. Reorder the terms: -10 + -3f + -1f + f2 = 10 + f + -10 + -1f Combine like terms: -3f + -1f = -4f -10 + -4f + f2 = 10 + f + -10 + -1f Reorder the terms: -10 + -4f + f2 = 10 + -10 + f + -1f Combine like terms: 10 + -10 = 0 -10 + -4f + f2 = 0 + f + -1f -10 + -4f + f2 = f + -1f Combine like terms: f + -1f = 0 -10 + -4f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -4f + 10 + f2 = 0 + 10 Reorder the terms: -10 + 10 + -4f + f2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -4f + f2 = 0 + 10 -4f + f2 = 0 + 10 Combine like terms: 0 + 10 = 10 -4f + f2 = 10 The f term is -4f. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4f + 4 + f2 = 10 + 4 Reorder the terms: 4 + -4f + f2 = 10 + 4 Combine like terms: 10 + 4 = 14 4 + -4f + f2 = 14 Factor a perfect square on the left side: (f + -2)(f + -2) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (f + -2) equal to 3.741657387 and -3.741657387.Subproblem 1
f + -2 = 3.741657387 Simplifying f + -2 = 3.741657387 Reorder the terms: -2 + f = 3.741657387 Solving -2 + f = 3.741657387 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + f = 3.741657387 + 2 Combine like terms: -2 + 2 = 0 0 + f = 3.741657387 + 2 f = 3.741657387 + 2 Combine like terms: 3.741657387 + 2 = 5.741657387 f = 5.741657387 Simplifying f = 5.741657387Subproblem 2
f + -2 = -3.741657387 Simplifying f + -2 = -3.741657387 Reorder the terms: -2 + f = -3.741657387 Solving -2 + f = -3.741657387 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + f = -3.741657387 + 2 Combine like terms: -2 + 2 = 0 0 + f = -3.741657387 + 2 f = -3.741657387 + 2 Combine like terms: -3.741657387 + 2 = -1.741657387 f = -1.741657387 Simplifying f = -1.741657387Solution
The solution to the problem is based on the solutions from the subproblems. f = {5.741657387, -1.741657387}
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