Posted by John on Wednesday, April 23, 2008 at 9:49pm.
x^2 - 14 x + 13 = 30 y
x^2 - 14 x = 30 y - 13
x^2 - 14 x + 49 = 30 y + 36
(x-7)^2 = 30 y + 36
x - 7 = +/- sqrt (30 y + 36)
x = 7 +/- sqrt (30 y + 36)
This is so much harder than your other question that I suspect a typo by the way.
x^2 - 14 x + 13 = 30 y
x^2 - 14 x = 30 y - 13
x^2 - 14 x + 49 = 30 y + 36 ****
(x-7)^2 = 30 y + 36
x - 7 = +/- sqrt (30 y + 36)
x = 7 +/- sqrt (30 y + 36)
where did you get the 49 or 36
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
(x-7)^2 = something + 49
x - 7 = +/- sqrt (something + 49)
by taking half the second coefficient and squaring it, I get a perfect square.
and 49 - 13 = 36
why is this not correct
30y = x^2 - 14x + 13
- 13
30y - 13 = x^2 - 14x
_________ ___________
-14 -14
x = sqrt 30y-13
_______
-14
Im really trying to follow your work... This is what I got the first time I tried before i asked...
sorry the division signs didn't line up correctly