Posted by John on .
solve for X 30y=x^214x+13

Math 
Damon,
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) 
Math 
Damon,
This is so much harder than your other question that I suspect a typo by the way.

Math 
John,
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,
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,
and 49  13 = 36

Math 
JOHN,
why is this not correct
30y = x^2  14x + 13
 13
30y  13 = x^2  14x
_________ ___________
14 14
x = sqrt 30y13
_______
14
Im really trying to follow your work... This is what I got the first time I tried before i asked... 
Math 
JOHN,
sorry the division signs didn't line up correctly