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Simplifying f(f + -8) = 56 Reorder the terms: f(-8 + f) = 56 (-8 * f + f * f) = 56 (-8f + f2) = 56 Solving -8f + f2 = 56 Solving for variable 'f'. Reorder the terms: -56 + -8f + f2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + -8f + f2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -8f + 56 + f2 = 0 + 56 Reorder the terms: -56 + 56 + -8f + f2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -8f + f2 = 0 + 56 -8f + f2 = 0 + 56 Combine like terms: 0 + 56 = 56 -8f + f2 = 56 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 = 56 + 16 Reorder the terms: 16 + -8f + f2 = 56 + 16 Combine like terms: 56 + 16 = 72 16 + -8f + f2 = 72 Factor a perfect square on the left side: (f + -4)(f + -4) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (f + -4) equal to 8.485281374 and -8.485281374.Subproblem 1
f + -4 = 8.485281374 Simplifying f + -4 = 8.485281374 Reorder the terms: -4 + f = 8.485281374 Solving -4 + f = 8.485281374 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 = 8.485281374 + 4 Combine like terms: -4 + 4 = 0 0 + f = 8.485281374 + 4 f = 8.485281374 + 4 Combine like terms: 8.485281374 + 4 = 12.485281374 f = 12.485281374 Simplifying f = 12.485281374Subproblem 2
f + -4 = -8.485281374 Simplifying f + -4 = -8.485281374 Reorder the terms: -4 + f = -8.485281374 Solving -4 + f = -8.485281374 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 = -8.485281374 + 4 Combine like terms: -4 + 4 = 0 0 + f = -8.485281374 + 4 f = -8.485281374 + 4 Combine like terms: -8.485281374 + 4 = -4.485281374 f = -4.485281374 Simplifying f = -4.485281374Solution
The solution to the problem is based on the solutions from the subproblems. f = {12.485281374, -4.485281374}
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