and please show your work so I can learn


  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 =\frac{-b+\sqrt{b^2}-4ac }{2a} , \frac{-b-\sqrt{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=\frac{6+2\sqrt{(-6)^2-4(y^2+14y-1)} }{2} , x=\frac{6-\sqrt{(-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=\frac{6+2\sqrt{10-y^2-14y} }{2}, x = \frac{6-2\sqrt{10-y^2-14y} }{2}

    Now that’s get us to the final solution:

    x=3+\sqrt{10-y^2-14y}, x=3-\sqrt{10-y^2-14y}

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

    Take care!


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