Question

I need help with this I need to know what I’m doing wrong.. do I need to put a negative for (y+8^2) or a positive 8 so confused… help #4

Answer 1

( x + 5)^2 + y^2 = 41

Explanation:

The equation we have is

`x^2+10x+y^2-16=0`

Let us add 25 to both sides

`x^2+10x+y^2-16+25=25`

A bit of rewriting gives

`(x^2+10x+25)+y^2-16=25`

Since x^2 + 10x + 25 = ( x+ 5)^2, the above becomes

`(x+5)^2+y^2-16=25`

Adding 16 to both sides gives

`(x+5)^2+y^2=25+16`
`\boxed{\left(x+5\right)^2+y^2=41.}`

which is our final answer!