Can someone please explain how to do this physics problem

The mass of the earth is 5.98 * 10^24 kg, the mass of the moon is 7.36 * 10^22 kg, and the distance between the centers of the earth and the moon is 3.82 * 10^8 m. How far is the center of mass of the earth-moon system from the center of the earth?

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DATA GIVEN
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First, Let us consider the line joining Earth and Moon as X-axis with Earth at the origin.
Co-ordinate of Earth = (0,0)
Co-ordinate of Moon = (3.82 x 10^8 , 0)
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SOLVING LOGIC
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Then,
Co-ordinate of center of mass of (Earth + Moon) System :
[ (m1x1 + m2x2) / (m1+m2) , (m1y1 + m2y2) / (m1+m2) ]...................( i )
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PUTTING THE VALUES AND SOLVING
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m1x1 --> mass of Earth * (X-co-ordinate of Earth) = m1*0 = 0
m2x2 ---> mass of Moon * (X-co-ordinate of Moon) = (7.36 * 10^22)*(3.82 * 10^8) = 2.81152 x 10^31
m1y1 --> mass of Earth * (Y-co-ordinate of Earth) = m1*0 = 0
m2y2 ---> mass of Moon * (Y-co-ordinate of Moon) = m2*0 = 0
m1+m2 = 5.98 * 10^24 + 7.36 * 10^22 = 6.0536 x 10^24

Putting values, we have ----->
[ (2.81152 x 10^31) / (6.0536 x 10^24) , 0 ]
= ( 4.644 x 10^6 , 0 ) ---> this is the co-ordinate of center of mass of system.
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FINAL RESULT
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So, center of mass of system is 4.644 x 10^6 meters away i.e. 4644 km away
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Mearth x X = Mmoon x (d-X)

5.98 x 10^24 X = 7.36 x 10^22 ( 3.82x 10^8 - X)

6.054 x 10^24 X = 2.81 x 10^31 and X = 4644 km (which is somewhere inside the Earth !!)