  We present high-contrast Magellan adaptive optics (MagAO) images of HD 7449,
a Sun-like star with one planet and a long-term radial velocity (RV) trend. We
unambiguously detect the source of the long-term trend from 0.6-2.15 \microns
~at a separation of \about 0\fasec 54. We use the object's colors and spectral
energy distribution to show that it is most likely an M4-M5 dwarf (mass \about
0.1-0.2 \msun) at the same distance as the primary and is therefore likely
bound. We also present new RVs measured with the Magellan/MIKE and PFS
spectrometers and compile these with archival data from CORALIE and HARPS. We
use a new Markov chain Monte Carlo procedure to constrain both the mass ($>
0.17$ \msun ~at 99$\%$ confidence) and semimajor axis (\about 18 AU) of the M
dwarf companion (HD 7449B). We also refine the parameters of the known massive
planet (HD 7449Ab), finding that its minimum mass is $1.09^{+0.52}_{-0.19}$
\mj, its semimajor axis is $2.33^{+0.01}_{-0.02}$ AU, and its eccentricity is
$0.8^{+0.08}_{-0.06}$. We use N-body simulations to constrain the eccentricity
of HD 7449B to $\lesssim$ 0.5. The M dwarf may be inducing Kozai oscillations
on the planet, explaining its high eccentricity. If this is the case and its
orbit was initially circular, the mass of the planet would need to be
$\lesssim$ 1.5 \mj. This demonstrates that strong constraints on known planets
can be made using direct observations of otherwise undetectable long-period
companions.
