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Simplifying (f + -7)(f + -10) = 0 Reorder the terms: (-7 + f)(f + -10) = 0 Reorder the terms: (-7 + f)(-10 + f) = 0 Multiply (-7 + f) * (-10 + f) (-7(-10 + f) + f(-10 + f)) = 0 ((-10 * -7 + f * -7) + f(-10 + f)) = 0 ((70 + -7f) + f(-10 + f)) = 0 (70 + -7f + (-10 * f + f * f)) = 0 (70 + -7f + (-10f + f2)) = 0 Combine like terms: -7f + -10f = -17f (70 + -17f + f2) = 0 Solving 70 + -17f + f2 = 0 Solving for variable 'f'. Factor a trinomial. (7 + -1f)(10 + -1f) = 0Subproblem 1
Set the factor '(7 + -1f)' equal to zero and attempt to solve: Simplifying 7 + -1f = 0 Solving 7 + -1f = 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 + -1f = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1f = 0 + -7 -1f = 0 + -7 Combine like terms: 0 + -7 = -7 -1f = -7 Divide each side by '-1'. f = 7 Simplifying f = 7Subproblem 2
Set the factor '(10 + -1f)' equal to zero and attempt to solve: Simplifying 10 + -1f = 0 Solving 10 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1f = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1f = 0 + -10 -1f = 0 + -10 Combine like terms: 0 + -10 = -10 -1f = -10 Divide each side by '-1'. f = 10 Simplifying f = 10Solution
f = {7, 10}
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