Posted by Lee on Wednesday, October 31, 2012 at 10:51am.
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 (x-a)^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:
(x-3/2)^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.
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