# Changing the subject of an equation.

• Apr 13th 2008, 11:44 AM
Mymble
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.
• Apr 13th 2008, 11:52 AM
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 ;)
• Apr 13th 2008, 12:00 PM
Mymble
Quote:

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!
• Apr 13th 2008, 12:04 PM
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 :)
• Apr 13th 2008, 12:12 PM
Mymble
Quote:

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?
• Apr 13th 2008, 12:15 PM
Moo
I changed the order of the terms on the left hand side of the equation when multiplying by (-1) :)
• Apr 13th 2008, 12:33 PM
Mymble
Quote:

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.