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Simplifying 8f2 + 4f + -7 = 0 Reorder the terms: -7 + 4f + 8f2 = 0 Solving -7 + 4f + 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 + 0.5f + f2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 0.5f + 0.875 + f2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 0.5f + f2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 0.5f + f2 = 0 + 0.875 0.5f + f2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 0.5f + f2 = 0.875 The f term is 0.5f. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5f + 0.0625 + f2 = 0.875 + 0.0625 Reorder the terms: 0.0625 + 0.5f + f2 = 0.875 + 0.0625 Combine like terms: 0.875 + 0.0625 = 0.9375 0.0625 + 0.5f + f2 = 0.9375 Factor a perfect square on the left side: (f + 0.25)(f + 0.25) = 0.9375 Calculate the square root of the right side: 0.968245837 Break this problem into two subproblems by setting (f + 0.25) equal to 0.968245837 and -0.968245837.Subproblem 1
f + 0.25 = 0.968245837 Simplifying f + 0.25 = 0.968245837 Reorder the terms: 0.25 + f = 0.968245837 Solving 0.25 + f = 0.968245837 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + f = 0.968245837 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + f = 0.968245837 + -0.25 f = 0.968245837 + -0.25 Combine like terms: 0.968245837 + -0.25 = 0.718245837 f = 0.718245837 Simplifying f = 0.718245837Subproblem 2
f + 0.25 = -0.968245837 Simplifying f + 0.25 = -0.968245837 Reorder the terms: 0.25 + f = -0.968245837 Solving 0.25 + f = -0.968245837 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + f = -0.968245837 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + f = -0.968245837 + -0.25 f = -0.968245837 + -0.25 Combine like terms: -0.968245837 + -0.25 = -1.218245837 f = -1.218245837 Simplifying f = -1.218245837Solution
The solution to the problem is based on the solutions from the subproblems. f = {0.718245837, -1.218245837}
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