algebra
posted by Lee on .
Solve the quadratic equation by completing the square.
3x^2+9x=1
Not sure how to do these, if someone could expplain.

it's usually easier to have a positive coefficient for x^2, so let's take care of that first:
3x^2  9x = 1
x^2  3x = 1/3
since (xa)^2 = x^2  2a + a^2, you want to take half of 3 and square it, then add that to both sides:
x^2  3x + 9/4 = 1/3 + 9/4
Now you have a perfect square on the left:
(x3/2)^2 = 23/12
now take square roots:
x  3/2 = ±√(23/12) = ±√69/6
so,
x = 3/2 ±√69/6
or,
x = (9±√69)/6
Note how that is the solution using the quadratic formula. 
Still confused, but I'll try another one and see if I get it. Thank you.