jmc

We would like to factor the left-hand side in the form $$(x^2-\boxed{})(x^2-\boxed{}).$$ The numbers in the boxes must multiply to give $225$ and add to give $34$. We write $225=3\cdot 3\cdot 5\cdot 5$ and try a few different pairs until we find that 9 and 25 satisfy the requirements. We factor further using difference of squares and solve. $$\begin{array}{rl}(x^2-9)(x^2-25)& =0\\ (x+3)(x-3)(x-5)(x+5)& =0\\ x=\pm 3,x=\pm 5& \end{array}$$ The smallest of these solutions is $x=\boxed{-5}$.