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

1 Answer

Answer:

#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)