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Simplifying (f + -11)(f + -13) = 0 Reorder the terms: (-11 + f)(f + -13) = 0 Reorder the terms: (-11 + f)(-13 + f) = 0 Multiply (-11 + f) * (-13 + f) (-11(-13 + f) + f(-13 + f)) = 0 ((-13 * -11 + f * -11) + f(-13 + f)) = 0 ((143 + -11f) + f(-13 + f)) = 0 (143 + -11f + (-13 * f + f * f)) = 0 (143 + -11f + (-13f + f2)) = 0 Combine like terms: -11f + -13f = -24f (143 + -24f + f2) = 0 Solving 143 + -24f + f2 = 0 Solving for variable 'f'. Factor a trinomial. (11 + -1f)(13 + -1f) = 0Subproblem 1
Set the factor '(11 + -1f)' equal to zero and attempt to solve: Simplifying 11 + -1f = 0 Solving 11 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1f = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1f = 0 + -11 -1f = 0 + -11 Combine like terms: 0 + -11 = -11 -1f = -11 Divide each side by '-1'. f = 11 Simplifying f = 11Subproblem 2
Set the factor '(13 + -1f)' equal to zero and attempt to solve: Simplifying 13 + -1f = 0 Solving 13 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1f = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1f = 0 + -13 -1f = 0 + -13 Combine like terms: 0 + -13 = -13 -1f = -13 Divide each side by '-1'. f = 13 Simplifying f = 13Solution
f = {11, 13}
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