= Solution
The autoregressive polynomial factors as $(1-0.4z)(1+0.7z)$, with zeros
$$
\boxed{z=2.5,\qquad z=-10/7.}
$$
Both have modulus greater than one. The <causality root criterion for an autoregressive model> therefore gives a causal stationary solution. The moving-average polynomial has its only zero at $-2$, also outside the unit circle, so the <invertibility of a moving-average model> holds. There is no common root to cancel.
To use unit-<variance> <white noise>, put $W_t=Z_t/2$. One suitable pair is
$$
\boxed{\widetilde\phi(z)=1+0.30z-0.28z^2,\qquad\widetilde\theta(z)=2+z.}
$$
Then $\widetilde\phi(B)X_t=\widetilde\theta(B)W_t$ with $W\sim\operatorname{WN}(0,1)$. The factor two changes the innovation scale, not the zero of the moving-average polynomial.
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