Creating two branches with similar current using capacitors/resistors
\$X\$ represents reactance not impedance. Impedance offered by capacitance is \$-jX_C\$ and it is a complex value. 

So the impedance offered by  branch-1 is \$-jX_{C_1}\$ and that offered by branch-2 is  \$-jX_{C_2} + R_2\$

For equal current to flow through these branches, the magnitude of impedances should be equal. ie.,

$$|-jX_{C_1}| = |-jX_{C_2} + R_2|$$
$$R_2 = \sqrt{X^2_{C_1} - X^2_{C_2}}$$
$$R_2 = \sqrt{1560.34^2-564.38^2} = 1454.69\Omega$$

You missed the \$-j\$ and wrote \$X_{C_1} = X_{C_2} + R_2\$ . That made the calculations go wrong.