Posted by Math 10 on Saturday, October 31, 2009 at 10:04pm.
by completing the square method solve the equation.
x^22x1
can u factor it? when i did it it couldn't be factored. i also don't know why it is not factorable because its a perfect square right?
please help me

Sameul  jim, Saturday, October 31, 2009 at 10:24pm
It can be factored, but not into integers like (x1); more like sqrt(2)+1, and it's definitely not a perfect square. I suspect you've got one of the signs backwards in your head, and you'll probably recognise that as we work through it.
Anyway, direct factorisation wasn't the question; this one is about completing the square.
Forget the constant for a minute, and focus on x^22x.
x^22x+c is a square. We just have to find c.
We know that
(x+a)^2 = x^2 + 2ax + a^2
and we want
x^2  2x + c
so, comparing the coefficients:
2a = 2
a = 1
(x1)^2 = x^2  2x + 1
Our expression is 2 less than that, so:
x^22x1 = (x1)^2  2
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