Find the non-extraneous solutions of the square root of the quantity x plus 6 minus 5 equals quantity x plus 1. x = −2 x = −6 and x = −5 x = −6 and x = −2 x = 2

The radical equation is .

i) We first isolate the square root, adding 5 to both sides of the equation: 
       
                                       

ii) Here let's substitute x+6 with t. Doing so we have:
 
                                         

Squaring both sides, we get:
                       
                                               

iii) Collecting the variables on the same side, and factorizing t we have:
 
                                               , which yields

                              t=0    or       t=1.

Now we solve for x in x+6=t:

x+6=0 ⇒x=-6       and x+6=1⇒x=-5.

iv) Now we check these values in the original equation   :

a)  ⇒ 0=0 ; Correct.

b)  ⇒ 1=1 ; Correct.

 x = −6 and x = −5