Posted by JOHN on Wednesday, April 23, 2008 at 10:08pm.
x^2  14 x + 13 = 30 y
x^2  14 x = 30 y  13
x^2  14 x + 49 = 30 y + 36 ****
(x7)^2 = 30 y + 36
x  7 = +/ sqrt (30 y + 36)
x = 7 +/ sqrt (30 y + 36)
where did you get the 49 or 36

Math  Damon, Wednesday, April 23, 2008 at 10:14pm
I did it below after you asked

Math  Damon, Wednesday, April 23, 2008 at 10:16pm
Here again:
========
#
Completing the square
x^2 + a x = something
x^2 + a x + (a/2)^2 = something + (a/2)^2
so
if
x^2 14 x = something
then
x^2  14 x +(14/2)^2 = something + (14/2)^2
or
x^2  14 x + 49 = something + 49
(x7)^2 = something + 49
x  7 = +/ sqrt (something + 49)
by taking half the second coefficient and squaring it, I get a perfect square.
# Math  Damon, Wednesday, April 23, 2008 at 10:13pm
and 49  13 = 36
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