Making $x$ the subject of $x^3-2x+y=1$ How to I make x the subject of this formula?
$$x^3-2x+y=1\tag1$$
My attempt:
I apply complete the square
$$(x-1)^3+y-1=1\tag2$$
$$(x-1)^3=2-y\tag3$$
$$x-1=\sqrt[3]{2-y}\tag4$$
$$x=1+\sqrt[3]{2-y}\tag5$$
but my teacher said it is wrong!
Can you please help? Thank in advance!

You make a mistake in the first step when you attempt to complete the square. Remember: you are working with an $x^3$, not an $x^2$, and because of this, any "completing of the cube" would require an $ax^2$ term as well. Unfortunately, due to the fact that $x^3 - 2x + y = 1$ is not one-to-one, there is no easy way to rewrite your function in the form $x = f(y)$.
