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Simplifying 8f2 + -6f + -7 = 0 Reorder the terms: -7 + -6f + 8f2 = 0 Solving -7 + -6f + 8f2 = 0 Solving for variable 'f'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + -0.75f + f2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -0.75f + 0.875 + f2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -0.75f + f2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -0.75f + f2 = 0 + 0.875 -0.75f + f2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -0.75f + f2 = 0.875 The f term is -0.75f. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75f + 0.140625 + f2 = 0.875 + 0.140625 Reorder the terms: 0.140625 + -0.75f + f2 = 0.875 + 0.140625 Combine like terms: 0.875 + 0.140625 = 1.015625 0.140625 + -0.75f + f2 = 1.015625 Factor a perfect square on the left side: (f + -0.375)(f + -0.375) = 1.015625 Calculate the square root of the right side: 1.007782219 Break this problem into two subproblems by setting (f + -0.375) equal to 1.007782219 and -1.007782219.Subproblem 1
f + -0.375 = 1.007782219 Simplifying f + -0.375 = 1.007782219 Reorder the terms: -0.375 + f = 1.007782219 Solving -0.375 + f = 1.007782219 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + f = 1.007782219 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + f = 1.007782219 + 0.375 f = 1.007782219 + 0.375 Combine like terms: 1.007782219 + 0.375 = 1.382782219 f = 1.382782219 Simplifying f = 1.382782219Subproblem 2
f + -0.375 = -1.007782219 Simplifying f + -0.375 = -1.007782219 Reorder the terms: -0.375 + f = -1.007782219 Solving -0.375 + f = -1.007782219 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + f = -1.007782219 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + f = -1.007782219 + 0.375 f = -1.007782219 + 0.375 Combine like terms: -1.007782219 + 0.375 = -0.632782219 f = -0.632782219 Simplifying f = -0.632782219Solution
The solution to the problem is based on the solutions from the subproblems. f = {1.382782219, -0.632782219}
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