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Simplifying 4f2 + 24f + -64 = 0 Reorder the terms: -64 + 24f + 4f2 = 0 Solving -64 + 24f + 4f2 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '4'. 4(-16 + 6f + f2) = 0 Factor a trinomial. 4((-8 + -1f)(2 + -1f)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-8 + -1f)' equal to zero and attempt to solve: Simplifying -8 + -1f = 0 Solving -8 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1f = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1f = 0 + 8 -1f = 0 + 8 Combine like terms: 0 + 8 = 8 -1f = 8 Divide each side by '-1'. f = -8 Simplifying f = -8Subproblem 2
Set the factor '(2 + -1f)' equal to zero and attempt to solve: Simplifying 2 + -1f = 0 Solving 2 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1f = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1f = 0 + -2 -1f = 0 + -2 Combine like terms: 0 + -2 = -2 -1f = -2 Divide each side by '-1'. f = 2 Simplifying f = 2Solution
f = {-8, 2}
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