I don't understand this question!
All it says is:
Complete the square to rewrite the following equation. Identify the center and radius of the circle. You must show all work and calculations to receive credit.

x^2 + 2x + y^2 + 4y = 20

x^2 + 2x + y^2 + 4y = 20

Let's break it into 2 parts.

x^2 + 2x and y^2 + 4y

What do you need to add to x^2 + 2x to make it a square of a binomial? It's the square of half the coefficient of x. In other words, (2/2) ^ 2, which is 1. So, you add 1.

x^2 + 2x + 1

Do the same for y^2 + 4y. (4/2) ^ 2 = 2^2 = 4. So, we add 4.

y^2 + 4y + 4.

But, we added a 1 and a 4. These can't just come out of nowhere. So, we need to add a 1 and a 4 to the other side of the equation as well. Right now, we have:

x^2 + 2x + 1 + y^2 + 4y + 4 = 20 + 1 + 4

What is x^2 +2x + 1 the square of? x + 1. How about y^2 + 4y + 4? x + 2. If we factor each of these and simplify the sum on the right side of the equation, we'll have rewritten the equation fully.

(x + 1)^2 + (y + 2)^2 = 25

Now, we need the center. Take the negative of the constant being added to each variable, and you'l have it. Here, we have 1 and 2. That means the center of the circle is (-1, -2).

How about the radius? It's the square root of that sum on the right side of the equation. The square root of 25 is 5, which is the radius.

pretty sure 750 each month!

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