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Simplifying f * f + 4f + -32 = 0 Multiply f * f f2 + 4f + -32 = 0 Reorder the terms: -32 + 4f + f2 = 0 Solving -32 + 4f + f2 = 0 Solving for variable 'f'. Factor a trinomial. (-8 + -1f)(4 + -1f) = 0Subproblem 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 '(4 + -1f)' equal to zero and attempt to solve: Simplifying 4 + -1f = 0 Solving 4 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1f = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1f = 0 + -4 -1f = 0 + -4 Combine like terms: 0 + -4 = -4 -1f = -4 Divide each side by '-1'. f = 4 Simplifying f = 4Solution
f = {-8, 4}
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