Question

How do you solve `5+2sqrt(5x+32)=12` and identify any restrictions?

Answer 1

`x=-79/20`

Explanation:

`5+2sqrt(5x+32)=12`
`2sqrt(5x+32)=7`
`sqrt(5x+32)=7/2`
`5x+32=+-(7/2)^2`
`5x=+-(7/2)^2-32`
`x=1/5(+-49/4-32)`
`x=-79/20,-177/20`

Plug them into the equation and check:
1.-79/20
`5+2sqrt(5*-79/20+32)=12`
`5+2sqrt(49/4)=12`
`5+2*7/2=12`
`5+7=12`
`12=12`
(This one works)

2.-177/20
`5+2sqrt(5*-177/20+32)=12`
`5+2sqrt(-49/4)=12`
(This one doesn't work since you can't have a negative square)