Solving one variable in terms of the another

Question

Let $y = x^2 - 2x + 6$. Express $x$ in terms of $y$.

This is my working:

$$ x^2 - 2x = y - 6, \\ x(x-2)= y - 6. $$

From this point, I got stuck as I can't fully factorize the $x$ out as seen above...

Thanks for the hint, if any...

Answer 1

Suggest you complete the square. You have $x^2-2x+1=Y-5,$ so $(x-1)^2=Y-5,$ then $x-1=\pm \sqrt{Y-5}$ and add $1$ to each side.

Note there was an error before last edit.

Answer 2

$$y=x^2-2x+6$$ $$x^2-2x+(6-y)=0$$ Thus, $$x=\frac{2\pm \sqrt{4-4(6-y)}}{2}$$ $$x={1\pm \sqrt{1-1(6-y)}}$$ $$x={1\pm \sqrt{y-5}}$$