i got you, buddy!
To rewrite the equation in standard form, we need to complete the square for both x and y terms.
Starting with the x terms: x^2 + 4x + y^2 - 10y = 7 (x^2 + 4x) + y^2 - 10y = 7 (x^2 + 4x + 4) + y^2 - 10y = 7 + 4 (adding and subtracting 4 to complete the square for x) (x + 2)^2 + y^2 - 10y = 11
Now completing the square for y terms: (x + 2)^2 + y^2 - 10y = 11 (x + 2)^2 + (y^2 - 10y + 25) = 11 + 25 (adding and subtracting 25 to complete the square for y) (x + 2)^2 + (y - 5)^2 = 36
Therefore, the equation in standard form is: (x + 2)^2 + (y - 5)^2 = 36