Answer:
(x + 1)² + (y + 1)² = (√6)²
Explanation:
Group the x- and y- terms together:
9x^2 + 18x + 9y^2 + 9y = 36
Factor out the coefficient 9:
x^2 + 2x + y^2 + y = 4
Complete the square of x^2 + 2x and then do the same for y^2 + 2y:
x^2 + 2x + 1 - 1 + y^2 + 2y + 1 - 1 = 4
Rewrite x^2 + 2x + 1 as the square of the binomial x + 1:
(x + 1)^2 + (y + 1)^2 - 2 = 4
Collect the constant terms on the right side:
(x + 1)^2 + (y + 1)^2 = 6
Rewrite 6 as (√6)^2:
(x + 1)² + (y + 1)² = (√6)² is the equation in standard form (x - h)² + (y - k)² = r²
Completing the square is done as follows: x^2 + 2x
Start with x^2 + 2x
1. Take half of the coefficient of x, which results in 2/2, or 1
2. Square this result and add it to, and subtract it from x^2 + 2x
x^2 + 2x + 1 - 1
3. Rewrite the first three terms as the square of a binomial:
x^2 + 2x + 1 - 1 = (x + 1)² - 1.
Do the same for y² + 2y.