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.

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 ;)

Quote:

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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 ;)

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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!

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 :)

Quote:

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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 :)

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Ok, thankyou.
One more thing... how does the x^2 get from being -x^2 to +x^2?

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

Quote:

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Originally Posted by Moo

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

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Ok.
I completely get it now :)
Thanks so much.