There are only two firms in an industry producing a homogeneous product and having identical production technology. The cost function of firm $i$ is
\[
C_i(q_i) = q_i^2, \quad \text{for } i = 1,2;
\]
where $q_i$ is the quantity produced by firm $i$. The market demand for the product is $p = 100 - q$, where $p$ is the unit price and $q = q_1 + q_2$ is the aggregate quantity. Assuming the firms are price takers, the competitive equilibrium solution of $p$ and $q$ in this market is