Answer
$C_1=5.74\mu F$
$C_2=29.26\mu F$
Work Step by Step
$C_1+C_2=35.0\mu F$
$C_1=35.0\mu F-C_2$
$\frac{1}{\frac{1}{C_1}+\frac{1}{C_2}}=4.8\mu F$
$\frac{1}{C_1}+\frac{1}{C_2}=\frac{1}{4.8\mu F}$
$\frac{C_2+C_1}{C_1C_2}=\frac{1}{4.8\mu F}$
$\frac{35.0\mu F}{35.0\mu FC_2-C_2^2}=\frac{1}{4.8\mu F}$
$35.0\mu FC_2-C_2^2=168\mu F$
Two solutions: $C_2=5.74\mu F$ and $C_2=29.26\mu F$
$C_1=5.74\mu F$
$C_2=29.26\mu F$
