I have been reviewing this question. : How can I find the points at which two circles intersect?
Although during the answering steps I got a little stuck:
From this:
17y2−62y+49=0
To this:
y=(31+82√)17
I am not 100% on the steps taken to achieve this transformation, could someone be so kind as to break down the steps you would follow to solve for y please?
I appreciate the time and help,
Thanks.
By the quadratic formula, whenever we have $ay^2+by+c=0,$ then $$y=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.$$ In particular, here, $a=17,b=-62,c=49.$ Now, $$(-62)^2-4(17)(49)=3844-3332=512=2\cdot256=2\cdot 16^2,$$ so we have $$y=\frac{-(-62)\pm\sqrt{2\cdot 16^2}}{2(17)}=\frac{62\pm16\sqrt2}{34}=\frac{31\pm8\sqrt2}{17}.$$
We can also use a method known as completing the square to get the job done.
