Transform the equation by completing the square:
y^2 + 2x - 6y - 7 = 0
y^2 - 6y +9 +2x = 7 +9
(y-3)^2 + 2x = 16
To complete the square for the given equation, follow these steps:
Step 1: Group the y-terms and the constant term separately.
y^2 - 6y + 2x - 7 = 0
Step 2: Move the constant term (in this case, -7) to the other side of the equation.
y^2 - 6y + 2x = 7
Step 3: Complete the square by adding the square of half the coefficient of the y-term (6/2 = 3) to both sides of the equation.
y^2 - 6y + 9 + 2x = 7 + 9
The y^2 - 6y + 9 expression is a perfect square trinomial and can be factored as (y - 3)^2. Simplifying the right side:
(y - 3)^2 + 2x = 16
Now, the equation is in completed square form.