Question

Can someone help me please ??! :)

Answer 1

@UnkleRhaukus

Answer 2

Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit.

x2 + 2x + y2 + 4y = 20

Answer 3

use `completing the square` method

Answer 4

Yes

Answer 5

complete the square on the x terms first

x^2 + 2x = (x+ )^2 +

Answer 6

Right so far I got the first two steps down its the third step that is confusing me.

Answer 7

A circle centred at \((a,b)\), with radius \(r\) has the form

\[(x-a)^2 + (y-b)^2 =r^2\]

Answer 8

This is what i've been using to help me

Answer 9

yeah it's just like that

Answer 10

Right the part Im really confused on is step 3 and down

Answer 11

@goformit100

Answer 12

How can I help you ?

Answer 13

Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit.

x2 + 2x + y2 + 4y = 20

Answer 14

I need help how to use " completing the square method "

Answer 15

You think you could help me @goformit100

Answer 16

if you had \[z^2+6z\]
completing the square goes like this

\[(z+a)^2=z^2+2ax+a^2\]

\[z^2+6z +9= (z+3)^2\]
so
\[z^2+6z= (z+3)^2-9\]


So halve the z coefficient , and put that in the brackets for a,
then because the number term is missing , take it away form both sides

Answer 17

So to complete the square on the x terms first

x^2 + 2x


what is the x coefficient ?

what is half of this ?

Answer 18

you cant get much more help than that \(\large \uparrow\)

Answer 19

Im not really sure

Answer 20

\(\color{brown}{This}\) term is the x coefficient
\[x^2 + \color{brown}2x \]
Because it is the number x is multiplied by

Answer 21

ohh ok

Answer 22

This is so far what I have

Answer 23

x2 + 2x + y2 + 4y = 20
(x2 + 2x) + (y2 + 4y) = 20
(x2+2x-1)+(y2+4y-2) = 20 + 20+1
(x2+2x-1) + (y2+4y-2) = 41

Answer 24

nope, the idea is you want the terms in those brackets to be perfect squares

(x^2+2x-1) is not a perfect square

but
(x^2+2x+1) is , because is equals (x+1)^2

Answer 25

(y^2+4y-2) is not a perfect square either

Answer 26

sorry, I'm really not good at this. Could you please explain to me what I do for step three in-depth?

Answer 27

Start with just these terms x^2 + 2ax

Find the x coefficient; (a)
then halve this; (a/2)


x^2 + 2ax + a^2 = (x+a)^2

so

x^2 + 2ax = (x+a)^2-a^2

Answer 28

step 3
take the coefficient of the term in x divide by 2 then square that number.
that is the number you are adding to the inside of the quadratic so that it can be factored. since you are adding this amount to this side of the equation you need to add it to the other side as well.
follow the same process for the section with the y group
let me see what you have

Answer 29

@UnkleRhaukus thank you @Rubio101 post what you have

Answer 30

x2 + 2x + y2 + 4y = 20
(x2 + 2x) + (y2 + 4y) = 20

Answer 31

Thats what I have Im not if im right or not.

Answer 32

*sure

Answer 33

(x^2 + 2x) + (y^2 + 4y) = 20
is right so far ,

now you have to complete the squares

Answer 34

now follow the directions in the post that says step 3

Answer 35

(x2+2x-1)+(y2+4y-2)=20+(20+1)

Answer 36

Thats what I have is that right?

Answer 37

@UnkleRhaukus Find the x coefficient; (a)
then halve this; (a/2)


x^2 + 2ax + a^2 = (x+a)^2
coefficient is 2a when in half =1/2*2a = a

Answer 38

*ops, thanks for spotting that error of mine @triciaal

Answer 39

@Rubio101 you are adding +1 and +4

Answer 40

\(x^2+ax+y^2+by=c\\(x+\frac{a}{2})^2+(y+\frac{y}{2})^2=c+(\frac{a}{2})^2+(\frac{b}{2})^2\)

Answer 41

figure out what a,b are and you are done....

Answer 42

and c....

Answer 43

it should be painfully obvious that a = 2, b=4, and c=20

Answer 44

its always positive because when you square a -ve the result is +ve and when you multiply +ve the result is +ve

Answer 45

I get it now. Thank you all. sorry if i was a bother

Answer 46

on the right hand side you are adding +1 and +4

Answer 47

it's ok you are not a bother we are here to help