# Thread: Changing the subject of an equation.

1. ## Changing the subject of an equation.

Could you help me with making x the subject of this equation please?

v^2 = w^2(a^2-x^2)

The answer in my text book is x = ((w^2 a^2 - v^2)^(1/2))/w
Sorry that may not make sense, I wasn't sure how to write it...

I've tried things like...

(v^2/w^2) = a^2 - x^2
(v^2/w^2) - a^2 = x^2

But never seem to get the right answer.

Thanks.

2. Hello,

You're in the right way

(v^2/w^2) = a^2 - x^2
(v^2/w^2) - a^2 = x^2

-> this is false, it's (v^2/w^2) - a^2 = -x^2

So a^2 - (v^2/w^2) = x^2

Put it on the same denominator.

This will make :

(a²w²-v²)/w²=x²

So x=sqrt((a²w²-v²)/w²)=sqrt(a²w²-v²)/w

And sqrt is equivalent to ^(1/2)

I'm not sure my notations make sense... If necessary, i can make it easier to read

3. Originally Posted by Moo
Hello,

You're in the right way

(v^2/w^2) = a^2 - x^2
(v^2/w^2) - a^2 = x^2

-> this is false, it's (v^2/w^2) - a^2 = -x^2

So a^2 - (v^2/w^2) = x^2

Put it on the same denominator.

This will make :

(a²w²-v²)/w²=x²

So x=sqrt((a²w²-v²)/w²)=sqrt(a²w²-v²)/w

And sqrt is equivalent to ^(1/2)

I'm not sure my notations make sense... If necessary, i can make it easier to read
Thanks, that makes sense.

Why is it that it's x = sqrt(a²w²-v²)/w not x = sqrt(aw-v)/w.
There's probably a really obvious reason, I just can't see it!

4. Because you keep the square :

x²=(a²w²-v²)/w²

Do you agree with it ?

so x=sqrt(a²w²-v²)/sqrt(w²) (assuming that x is positive)

And sqrt(w²)=w

You can't simplify a²w²-v², you can only factor it

5. Originally Posted by Moo
Because you keep the square :

x²=(a²w²-v²)/w²

Do you agree with it ?

so x=sqrt(a²w²-v²)/sqrt(w²) (assuming that x is positive)

And sqrt(w²)=w

You can't simplify a²w²-v², you can only factor it
Ok, thankyou.
One more thing... how does the x^2 get from being -x^2 to +x^2?

6. I changed the order of the terms on the left hand side of the equation when multiplying by (-1)

7. Originally Posted by Moo
I changed the order of the terms on the left hand side of the equation when multiplying by (-1)
Ok.
I completely get it now
Thanks so much.