Answer
{1, 9}
Work Step by Step
Reorder $z^{2}$ + 9 = 10z to $z^{2}$ -10z + 9.
1. Factor:
$z^{2}$ -10z + 9 = (z - 9)(z - 1)
2. Apply the zero factor property to the factored expression:
a) z - 9 = 0
b) z - 1 = 0
3. Solve each linear equation:
a) z = 9
b) z = 1
The solutions are {1, 9}.
