Question

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

Image of the equation: https://prnt.sc/s83fel

Answer 1

separate the x terms and the y terms

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

you want to create 2 perfect square trinomials (a^2 + 2ab + b^2, to be factored into (a+b)^2, one for the x terms and one for the y term

let's start with x^2 + 2x. take the x-term (2x), divide the coefficient by 2, square the result.

you get x^2 + 2x + 1, which factors into (x+1)^2. remember, you must also add 1 to the right side of the equation to keep things balance.

repeat this process with the y terms.

you should end up w/ a circle equation in the form (x-h)^2 + (y-k)^2 = r^2

find your (h,k) to get your circle center, and your r-value to get the radius.