Answer
The solutions are $1, 9$.
Work Step by Step
$z^{2}+9=10z$
Steps 1-3: not needed.
Step 4: The equation is quadratic
Step 5: Rewrite the equation in standard form.
$z^{2}-10z+9=0$
Step 6: Factor.
$(z - 1)(z-9)=0$
Step 7: Set each factor equal to 0.
$z - 1=0$ or $z-9=0$
Step 8: Solve each equation.
$z = 1$ or $z=9$
Final Step: Check by substituting into the original equation. The solutions are $1, 9$.
