# If the distance between (a ,3) and (4,2) is root 37, find the values of a

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Using the distance formula: `d = sqrt((x_(2) - x_(1))^2 + (y_(2) - y_(1))^2)` we can solve for "a".

So substituting in our given values for (x and y, we'd have:

`sqrt(37)=sqrt((4-a)^2 + (2-3)^2)` Square both sides.

`37 = (4-a)^2 + 1` Subtract 1

`36 = (4-a)^2` Take the square root of each side.

`+-6 = 4-a` Subtract 4.

`6-4 = -a` or `-6-4 = -a`

`2 = -a` or `-10 = -a`

`a = -2` ** or** a = 10