# Thread: Make x the subject of y(x^2+a^2)=a^3

1. ## Make x the subject of y(x^2+a^2)=a^3

Make x the subject of y(x^2+a^2)=a^3
Many Thanks!

2. Originally Posted by BabyMilo
Many Thanks!
You want to solve $\displaystyle y(x^2+ a^2)= a^3$ for a.

Okay, multiplying the left side, $\displaystyle x^2y+ a^2y= a^3$ which is the same as $\displaystyle a^3- ya^2- x^2y= 0$. That is a cubic equation and there is a formula for the solution- unfortunately, it is very complicated.

Look at Cubic Formula -- from Wolfram MathWorld

3. I appreciate your help! But I am just making x the subject (like rearranging the equation). Many Thanks!

4. Originally Posted by BabyMilo
I appreciate your help! But I am just making x the subject (like rearranging the equation). Many Thanks!
Divide by y. Subtract a^2. Take the square root.

5. Originally Posted by mr fantastic
Divide by y. Subtract a^2. Take the square root.
so would it be? x=sq root of (a^3/y)-a^2 Many THanks!

6. Originally Posted by BabyMilo
so would it be? x=sq root of (a^3/y)-a^2 Many THanks!
You need $\displaystyle \pm \sqrt{}$