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Simplifying 20f2 + 90 = 110f Reorder the terms: 90 + 20f2 = 110f Solving 90 + 20f2 = 110f Solving for variable 'f'. Reorder the terms: 90 + -110f + 20f2 = 110f + -110f Combine like terms: 110f + -110f = 0 90 + -110f + 20f2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(9 + -11f + 2f2) = 0 Factor a trinomial. 10((1 + -1f)(9 + -2f)) = 0 Ignore the factor 10.Subproblem 1
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 = 1Subproblem 2
Set the factor '(9 + -2f)' equal to zero and attempt to solve: Simplifying 9 + -2f = 0 Solving 9 + -2f = 0 Move all terms containing f to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2f = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2f = 0 + -9 -2f = 0 + -9 Combine like terms: 0 + -9 = -9 -2f = -9 Divide each side by '-2'. f = 4.5 Simplifying f = 4.5Solution
f = {1, 4.5}
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