Expert: Abe Mantell - 8/14/2010

Question
The equation is 2x^2-6x+3=0. I'm having problems mainly because of the -6x in the middle. I've followed all the examples in my book on how to solve and understand that it is most likely an irrational answer I'd have to use my calculator for but nothing seems to work out to get the answer in my answer book. My answer book says 2.37 and 0.63 are the answers but I have no idea how to get there. Could you please help me? Thank you.

Answer
Hello Emily,

Do you know how to factor quadratics?  If so, and you tried, you
would find that this is not factorable!  Thus, just use the
quadratic formula.  That is, for ax^2+bx+c=0,
x=(-b "+ or -" sqrt(b^2-4ac))/(2a)
In this case, a=2, b=-6, and c=3...thus,
x=(6 "+ or -" sqrt(36-4*2*3))/4
=(6 "+ or -" sqrt(12))/4
=(6 "+ or -" 2*sqrt(3))/4
= 3/2 "+ or -" sqrt(3)/2
which gives about 0.6339745960 and 2.366025404

I hope this helps!  :-)

TTYL, Abe