Question

X²+y²-6x+14y-1=0
and please show your work so I can learn

Answer 1

Hello there,

I hope you and your family are staying safe and healthy during this winter season.

`x^2 + y^2 -6x+14y-1=0`

We need to use the Quadratic Formula*

`x =(-b+√(b^2)-4ac )/(2a)` ,
`(-b-√(b^2) -4ac )/(2a)`

Thus, given the problem:

`a = 1, b=-6, c=y^2+14y-1`

So now we just need to plug them in the Quadratic Formula*

`x=(6+2√((-6)^2-4(y^2+14y-1)) )/(2)` ,
`x=(6-√((-6)^2-4(y^2+14y-1)) )/(2)`

As you can see, it is a mess right now. Therefore, we need to simplify it

`x=(6+2√(10-y^2-14y) )/(2)`,
`x = (6-2√(10-y^2-14y) )/(2)`

Now that's get us to the final solution:

`x=3+√(10-y^2-14y)`,
`x=3-√(10-y^2-14y)`

It is my pleasure to help students like you! If you have additional questions, please let me know.

Take care!

~Garebear