Hello there,
I hope you and your family are staying safe and healthy during this winter season.
[tex]x^2 + y^2 -6x+14y-1=0[/tex]
We need to use the Quadratic Formula*
[tex]x =\frac{-b+\sqrt{b^2}-4ac }{2a}[/tex] , [tex]\frac{-b-\sqrt{b^2} -4ac }{2a}[/tex]
Thus, given the problem:
[tex]a = 1, b=-6, c=y^2+14y-1[/tex]
So now we just need to plug them in the Quadratic Formula*
[tex]x=\frac{6+2\sqrt{(-6)^2-4(y^2+14y-1)} }{2}[/tex] , [tex]x=\frac{6-\sqrt{(-6)^2-4(y^2+14y-1)} }{2}[/tex]
As you can see, it is a mess right now. Therefore, we need to simplify it
[tex]x=\frac{6+2\sqrt{10-y^2-14y} }{2}[/tex], [tex]x = \frac{6-2\sqrt{10-y^2-14y} }{2}[/tex]
Now that's get us to the final solution:
[tex]x=3+\sqrt{10-y^2-14y}[/tex], [tex]x=3-\sqrt{10-y^2-14y}[/tex]
It is my pleasure to help students like you! If you have additional questions, please let me know.
Take care!
~Garebear
