How to isolate x in a quadratic equation

[f24u7]

Homework Statement

I just would like to know how would I isolate x in a quadratic equation such as y = x(3-x).

Homework Equations

quadratic equation.

The Attempt at a Solution

I don't think you can use completing square in this, and quadratic equation doesn't really help much since I'm not solving for x.





Thanks in advance

 

[Slats18]

Assuming you're going to input values of x to find y, I think you can use the quadratic equation to get x as a function of y, and then use some algebra to create y as a function of x. The only problem would be you would get two answers for x as a function of y, so bouth would need to be considered. Try letting y be an arbitrary value and use the quadratic equation on this:
<br /> -x^2+3x-y=0<br />

 

[Strants]

Why couldn't you complete the square? Just multiply both sides by negative one, so you have
-y=x^2-3x, then go from there.

 

[HallsofIvy]

Homework Statement

I just would like to know how would I isolate x in a quadratic equation such as y = x(3-x).

Homework Equations

quadratic equation.

The Attempt at a Solution

I don't think you can use completing square in this, and quadratic equation doesn't really help much since I'm not solving for x.

On the contrary, you are solving for x! To solve an equation for x means to write it as x= ... where there is no "x" on the right. And that is exactly what you mean by "isolating x".

y= x(3- x)= 3x- x^2 so that x^2- 3x+ y= 0. Use the quadratic formula,
\frac{-b\pm\sqrt{b^2- 4ac}}{2a}
with a= 1, b= -3 and c= y. The fact that c is "y" rather than a specific number just means that your solution will depend upon y.

Thanks in advance

 

[pongo38]

Have you tried drawing the graph?