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.

x2 + 2x + y2 + 4y = 20

Answer 1

you might want to write that into the standard form of a circle:
\[ (x−h)^2+(y−k)^2=r^2\]

Answer 2

how would i do that tho

Answer 3

you are given:
\[x^2 + 2x + y^2 + 4y = 20\]
you can separate that into paranthesis, as it doesnt really change anything:
\[ ( x^2 + 2x) +( y^2 + 4y) = 20 \]
now you should convert x to square form:
\[ (x^2+2x+1)+(y^2+4y)=20+1 \Rightarrow (x+1)^2+(y^2+4y)=20+1 \]
now you can do the same for y:
\[ (x+1)^2+(y^2+4y+4)=20+1+4 \Rightarrow (x+1)^2+(y+2)^2=25 \]
last thing to do is to get radius in exponential form -- basically just find the square root of 25:
\[ \sqrt{25} =5 \]
thus, final it would be:
\[ (x+1)^2+(y+2)^2=5^2 \]
compare that to \( (x−h)^2+(y−k)^2=r^2 ​\)
\( ( h, k ) \) is going to be the center, and \( r \) is the radi

Answer 4

i know the radius and allat, i just need the thing written in a different way