1. The problem is to perform nodal analysis on an electrical circuit to find the node voltages. 2. Nodal analysis uses Kirchhoff's Current Law (KCL), which states that the sum of currents leaving or entering a node is zero. 3. The general formula for current through a resistor is $I=\frac{V}{R}$, where $V$ is the voltage difference across the resistor and $R$ is the resistance. 4. Assign node voltages with respect to a reference node (ground). 5. Write KCL equations for each node except the reference node, expressing currents in terms of node voltages and resistances. 6. Solve the resulting system of linear equations to find the node voltages. 7. Example: For a node with voltage $V_1$ connected to ground through resistor $R_1$ and to another node $V_2$ through resistor $R_2$, KCL at $V_1$ is: $$\frac{V_1 - 0}{R_1} + \frac{V_1 - V_2}{R_2} = 0$$ 8. Repeat for all nodes, then solve the system using substitution or matrix methods. This method allows you to find all unknown node voltages in the circuit.