# Thread: need help understanding how to solve for x

1. ## need help understanding how to solve for x

$2x^2=1$

i divided by 2 to get $x^2=1/2$

then to get x i took the radical $\sqrt{x}=\sqrt{1}/\sqrt{2}$

but it doesn't make sense to me after that.

then eventual answer is $\sqrt{2}/2$

2. Originally Posted by rasczak
$2x^2=1$

i divided by 2 to get $x^2=1/2$

then to get x i took the radical $sqrtx=sqrt1/sqrt2$

but it doesn't make sense to me after that.
Technically you did isolate the variable x by saying that

$x=1/2\,\sqrt {2}$

It is standard practice to eliminate the radical in the denominator. In this case, multiply both the top and the bottom by radical 2, and you should be fine.

3. Originally Posted by arcketer
Technically you did isolate the variable x by saying that

$x=1/2\,\sqrt {2}$

It is standard practice to eliminate the radical in the denominator. In this case, multiply both the top and the bottom by radical 2, and you should be fine.
how did you come up with $x=1/2\,\sqrt {2}$?

my math came up with $x=1/\,\sqrt {2}$.

4. Originally Posted by rasczak
how did you come up with $x=1/2\,\sqrt {2}$?

my math came up with $x=1/\,\sqrt {2}$.
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

$x=1/2\,\sqrt {2}$

Let me know if this makes sense.

EDIT: Also, obviously, I assume you know that the square root of 1 is 1.

5. (sorry) Yes, arcketer, you found one solution but not the other :

$2x^2 = 1$

This is equivalent (obviously) to :

$x^2 = \frac{1}{2}$

Therefore, taking the square root yields :

$x = \sqrt{\frac{1}{2}}$ and $x = - \sqrt{\frac{1}{2}}$ (the square of a number is equal to the square of its opposite!)

Using properties of square roots, the solutions become :

$x = \frac{\sqrt{1}}{\sqrt{2}}$ and $x = - \frac{\sqrt{1}}{\sqrt{2}}$.

Simplifying :

$x = \frac{1}{\sqrt{2}}$ and $x = - \frac{1}{\sqrt{2}}$.

6. Yes I forgot the negative term when taking the square root, my mistake. However, 1 / root(2) is the same as root(2) / 2.

7. Originally Posted by arcketer
Yes I forgot the negative term when taking the square root, my mistake. However, 1 / root(2) is the same as root(2) / 2.
Yes, I edited, my bad. Sometimes I take too quick decisions

8. Originally Posted by Bacterius
Yes, I edited, my bad. Sometimes I take too quick decisions
No worries, mate

9. Originally Posted by arcketer
Yes I forgot the negative term when taking the square root, my mistake. However, 1 / root(2) is the same as root(2) / 2.
You will NEVER "[forget] the negative" if you use a procedure that makes you look at it.

$2x^{2} = 1$

$2x^{2} - 1 = 0$

$(\sqrt{2}x+1)(\sqrt{2}x-1) = 0$

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.

10. Originally Posted by arcketer
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

$x=1/2\,\sqrt {2}$

Let me know if this makes sense.

EDIT: Also, obviously, I assume you know that the square root of 1 is 1.
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.