Question

What equation results from completing the square and then factoring? x^2+22x=31 A.(x+22)^2=53 B.(x+22)^2=152 C.(x+11)^2=152 D.(x+11)^2=53

Answer 1

`\boxed{\mathrm{Option \ C}}`

Explanation:

=>
`x^2+22x = 31`

=>
`(x)^2+2(x)(11) = 31`

Since b = 11 , So
`(11)^2` needs to be added to both sides

Adding
`(11)^2` to both sides

=>
`(x)^2+2(x)(11)+(11)^2 = 31+(11)^2`

Completing the square

=>
`(x+11)^2 = 31+121`

=>
`(x+11)^2 = 152`