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Simplifying -4f2 + -64f = -44 Reorder the terms: -64f + -4f2 = -44 Solving -64f + -4f2 = -44 Solving for variable 'f'. Reorder the terms: 44 + -64f + -4f2 = -44 + 44 Combine like terms: -44 + 44 = 0 44 + -64f + -4f2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(11 + -16f + -1f2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(11 + -16f + -1f2)' equal to zero and attempt to solve: Simplifying 11 + -16f + -1f2 = 0 Solving 11 + -16f + -1f2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + 16f + f2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 16f + 11 + f2 = 0 + 11 Reorder the terms: -11 + 11 + 16f + f2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 16f + f2 = 0 + 11 16f + f2 = 0 + 11 Combine like terms: 0 + 11 = 11 16f + f2 = 11 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 = 11 + 64 Reorder the terms: 64 + 16f + f2 = 11 + 64 Combine like terms: 11 + 64 = 75 64 + 16f + f2 = 75 Factor a perfect square on the left side: (f + 8)(f + 8) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (f + 8) equal to 8.660254038 and -8.660254038.Subproblem 1
f + 8 = 8.660254038 Simplifying f + 8 = 8.660254038 Reorder the terms: 8 + f = 8.660254038 Solving 8 + f = 8.660254038 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 = 8.660254038 + -8 Combine like terms: 8 + -8 = 0 0 + f = 8.660254038 + -8 f = 8.660254038 + -8 Combine like terms: 8.660254038 + -8 = 0.660254038 f = 0.660254038 Simplifying f = 0.660254038Subproblem 2
f + 8 = -8.660254038 Simplifying f + 8 = -8.660254038 Reorder the terms: 8 + f = -8.660254038 Solving 8 + f = -8.660254038 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 = -8.660254038 + -8 Combine like terms: 8 + -8 = 0 0 + f = -8.660254038 + -8 f = -8.660254038 + -8 Combine like terms: -8.660254038 + -8 = -16.660254038 f = -16.660254038 Simplifying f = -16.660254038Solution
The solution to the problem is based on the solutions from the subproblems. f = {0.660254038, -16.660254038}Solution
f = {0.660254038, -16.660254038}
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