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Simplifying 7f2 + -1f + -5 = 0 Reorder the terms: -5 + -1f + 7f2 = 0 Solving -5 + -1f + 7f2 = 0 Solving for variable 'f'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + -0.1428571429f + f2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -0.1428571429f + 0.7142857143 + f2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -0.1428571429f + f2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -0.1428571429f + f2 = 0 + 0.7142857143 -0.1428571429f + f2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -0.1428571429f + f2 = 0.7142857143 The f term is -0.1428571429f. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429f + 0.005102040819 + f2 = 0.7142857143 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429f + f2 = 0.7142857143 + 0.005102040819 Combine like terms: 0.7142857143 + 0.005102040819 = 0.719387755119 0.005102040819 + -0.1428571429f + f2 = 0.719387755119 Factor a perfect square on the left side: (f + -0.07142857145)(f + -0.07142857145) = 0.719387755119 Calculate the square root of the right side: 0.848167292 Break this problem into two subproblems by setting (f + -0.07142857145) equal to 0.848167292 and -0.848167292.Subproblem 1
f + -0.07142857145 = 0.848167292 Simplifying f + -0.07142857145 = 0.848167292 Reorder the terms: -0.07142857145 + f = 0.848167292 Solving -0.07142857145 + f = 0.848167292 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + f = 0.848167292 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + f = 0.848167292 + 0.07142857145 f = 0.848167292 + 0.07142857145 Combine like terms: 0.848167292 + 0.07142857145 = 0.91959586345 f = 0.91959586345 Simplifying f = 0.91959586345Subproblem 2
f + -0.07142857145 = -0.848167292 Simplifying f + -0.07142857145 = -0.848167292 Reorder the terms: -0.07142857145 + f = -0.848167292 Solving -0.07142857145 + f = -0.848167292 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + f = -0.848167292 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + f = -0.848167292 + 0.07142857145 f = -0.848167292 + 0.07142857145 Combine like terms: -0.848167292 + 0.07142857145 = -0.77673872055 f = -0.77673872055 Simplifying f = -0.77673872055Solution
The solution to the problem is based on the solutions from the subproblems. f = {0.91959586345, -0.77673872055}
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