$\displaystyle 2x^2=1$
i divided by 2 to get $\displaystyle x^2=1/2$
then to get x i took the radical $\displaystyle \sqrt{x}=\sqrt{1}/\sqrt{2}$
but it doesn't make sense to me after that.
then eventual answer is $\displaystyle \sqrt{2}/2$
$\displaystyle 2x^2=1$
i divided by 2 to get $\displaystyle x^2=1/2$
then to get x i took the radical $\displaystyle \sqrt{x}=\sqrt{1}/\sqrt{2}$
but it doesn't make sense to me after that.
then eventual answer is $\displaystyle \sqrt{2}/2$
Remember that when you have a fraction, you can multiply it by the number 1, and the value will be unchanged. This is obvious, right?
In this case, we multiply the fraction by the square root of two, DIVIDED by the square root of two. Obviously, that is equal to one. Then, you just simplify.
On the denominator, you have the root of 2 multiplied by the root of 2, which is 2. On the top you get the square root of two, which is simply
$\displaystyle x=1/2\,\sqrt {2}$
Let me know if this makes sense.
EDIT: Also, obviously, I assume you know that the square root of 1 is 1.
(sorry) Yes, arcketer, you found one solution but not the other :
$\displaystyle 2x^2 = 1$
This is equivalent (obviously) to :
$\displaystyle x^2 = \frac{1}{2}$
Therefore, taking the square root yields :
$\displaystyle x = \sqrt{\frac{1}{2}}$ and $\displaystyle x = - \sqrt{\frac{1}{2}}$ (the square of a number is equal to the square of its opposite!)
Using properties of square roots, the solutions become :
$\displaystyle x = \frac{\sqrt{1}}{\sqrt{2}}$ and $\displaystyle x = - \frac{\sqrt{1}}{\sqrt{2}}$.
Simplifying :
$\displaystyle x = \frac{1}{\sqrt{2}}$ and $\displaystyle x = - \frac{1}{\sqrt{2}}$.
You will NEVER "[forget] the negative" if you use a procedure that makes you look at it.
$\displaystyle 2x^{2} = 1$
$\displaystyle 2x^{2} - 1 = 0$
$\displaystyle (\sqrt{2}x+1)(\sqrt{2}x-1) = 0$
How will you miss either solution?
There is a reason why you studied all that factoring. You were just stuck with integers and rational numbers.
unfortunately, a lot of this has left my brain. i haven't touched this material in fifteen years. I just started school this semester and i wasn't allowed to retake algebra ( passed it), so i took trig. I pretty far behind right now, but slowly getting back up to speed. I just hope i can catch up before the semester ends.