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...
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1Complete the square: $x^2-2x=(x-1)^2-1$ – J.R. Feb 19 '16 at 12:28
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For some values of $y$ there will be two solutions $x$, and for other values none. Think "quadratic formula" (and possibly visualize the graph of this equation, as a parabola). – hardmath Feb 19 '16 at 12:57
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$$y=x^2-2x+6$$ $$x^2-2x+(6-y)=0$$ Thus, $$x=\frac{2\pm \sqrt{4-4(6-y)}}{2}$$ $$x={1\pm \sqrt{1-1(6-y)}}$$ $$x={1\pm \sqrt{y-5}}$$
GoodDeeds
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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.
coffeemath
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Can I know why must we complete the square ? , thanks anyway for the help ! – user307640 Feb 19 '16 at 13:44