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Simplifying -2f2 + -28f + 94 = 0 Reorder the terms: 94 + -28f + -2f2 = 0 Solving 94 + -28f + -2f2 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '2'. 2(47 + -14f + -1f2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(47 + -14f + -1f2)' equal to zero and attempt to solve: Simplifying 47 + -14f + -1f2 = 0 Solving 47 + -14f + -1f2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -47 + 14f + f2 = 0 Move the constant term to the right: Add '47' to each side of the equation. -47 + 14f + 47 + f2 = 0 + 47 Reorder the terms: -47 + 47 + 14f + f2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 14f + f2 = 0 + 47 14f + f2 = 0 + 47 Combine like terms: 0 + 47 = 47 14f + f2 = 47 The f term is 14f. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14f + 49 + f2 = 47 + 49 Reorder the terms: 49 + 14f + f2 = 47 + 49 Combine like terms: 47 + 49 = 96 49 + 14f + f2 = 96 Factor a perfect square on the left side: (f + 7)(f + 7) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (f + 7) equal to 9.797958971 and -9.797958971.Subproblem 1
f + 7 = 9.797958971 Simplifying f + 7 = 9.797958971 Reorder the terms: 7 + f = 9.797958971 Solving 7 + f = 9.797958971 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + f = 9.797958971 + -7 Combine like terms: 7 + -7 = 0 0 + f = 9.797958971 + -7 f = 9.797958971 + -7 Combine like terms: 9.797958971 + -7 = 2.797958971 f = 2.797958971 Simplifying f = 2.797958971Subproblem 2
f + 7 = -9.797958971 Simplifying f + 7 = -9.797958971 Reorder the terms: 7 + f = -9.797958971 Solving 7 + f = -9.797958971 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + f = -9.797958971 + -7 Combine like terms: 7 + -7 = 0 0 + f = -9.797958971 + -7 f = -9.797958971 + -7 Combine like terms: -9.797958971 + -7 = -16.797958971 f = -16.797958971 Simplifying f = -16.797958971Solution
The solution to the problem is based on the solutions from the subproblems. f = {2.797958971, -16.797958971}Solution
f = {2.797958971, -16.797958971}
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