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Simplifying 45f2 + 24f + -189 = 0 Reorder the terms: -189 + 24f + 45f2 = 0 Solving -189 + 24f + 45f2 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '3'. 3(-63 + 8f + 15f2) = 0 Factor a trinomial. 3((-7 + -3f)(9 + -5f)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -3f)' equal to zero and attempt to solve: Simplifying -7 + -3f = 0 Solving -7 + -3f = 0 Move all terms containing f to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -3f = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3f = 0 + 7 -3f = 0 + 7 Combine like terms: 0 + 7 = 7 -3f = 7 Divide each side by '-3'. f = -2.333333333 Simplifying f = -2.333333333Subproblem 2
Set the factor '(9 + -5f)' equal to zero and attempt to solve: Simplifying 9 + -5f = 0 Solving 9 + -5f = 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 + -5f = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5f = 0 + -9 -5f = 0 + -9 Combine like terms: 0 + -9 = -9 -5f = -9 Divide each side by '-5'. f = 1.8 Simplifying f = 1.8Solution
f = {-2.333333333, 1.8}
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