Final answer:
To complete the square and write the equation in standard form, group the x-terms and the y-terms separately and add the square of half the coefficients. The equation (x + 4)² + (y + 1)² = 53 is in standard form. The center of the circle is (-4, -1) and the radius is √53.
Step-by-step explanation:
To complete the square and write the equation in standard form, we need to group the x-terms and the y-terms separately. Let's start with the x-terms. To complete the square for x² + 8x, we take half of the coefficient of x (which is 8) and square it. Half of 8 is 4, and 4 squared is 16. So we add 16 to both sides of the equation:
x² + 8x + 16 + y² + 2y + 1 = 36 + 16
Now, let's complete the square for the y-terms. We take half of the coefficient of y (which is 2) and square it. Half of 2 is 1, and 1 squared is 1. So we add 1 to both sides of the equation:
x² + 8x + 16 + y² + 2y + 1 + 1 = 36 + 16 + 1
This simplifies to:
(x + 4)² + (y + 1)² = 53
So the equation in standard form is (x + 4)² + (y + 1)² = 53. The center of the circle is (-4, -1) and the radius is √53.