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Simplifying 2f2 + 44f + -46 = 0 Reorder the terms: -46 + 44f + 2f2 = 0 Solving -46 + 44f + 2f2 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '2'. 2(-23 + 22f + f2) = 0 Factor a trinomial. 2((-23 + -1f)(1 + -1f)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-23 + -1f)' equal to zero and attempt to solve: Simplifying -23 + -1f = 0 Solving -23 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + -1f = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -1f = 0 + 23 -1f = 0 + 23 Combine like terms: 0 + 23 = 23 -1f = 23 Divide each side by '-1'. f = -23 Simplifying f = -23Subproblem 2
Set the factor '(1 + -1f)' equal to zero and attempt to solve: Simplifying 1 + -1f = 0 Solving 1 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1f = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1f = 0 + -1 -1f = 0 + -1 Combine like terms: 0 + -1 = -1 -1f = -1 Divide each side by '-1'. f = 1 Simplifying f = 1Solution
f = {-23, 1}
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