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

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Answer 1 · 2017-08-26T23:50:10

$x=-79/20$

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

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)

How do you solve 5+2sqrt(5x+32)=125+2sqrt(5x+32)=12 and identify any restrictions?