a reinterpretation of japhy's solution gives 54:

$_=pop;$l^$_?$l=$_:die"$_\n"while$_=($_+$ARGV[0]/$_)/2
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jynx

update: this works at 53:

$_=pop;$l^$_?$l=$_:die"$_\n"while($_+=$ARGV[0]/$_)/=2
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update2: using the comma instead of quotes for die it's 52:

$_=pop;$l^$_?$l=$_:die$_,$/while($_+=$ARGV[0]/$_)/=2
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