EXAMPLES. 

 {. Given .v^-|-4.Vi=:i4o ; to find X. 

 First, A,''-{-4A;+4m4o-f-4~i44 by completing the 

 square ; 



Then ^x ' -|-4A? + 4^\/ 1 44 try extracting the root ; 

 Or X'\-2—i2y 

 And therefore a;— 12 — 2=io. 



2. Given a;*— 6»V"|-8=8o ; to find x. 



First, x^ — 5Ars=8o — 8 = 72 by transposition ; 

 Then .v* — 6Ar+9zr 72-t-9=8i by completing the square 5 

 And X — 3= x/ 8 1 1=9 by extracting the root ; 

 Therefore ;ci=:9-j-3Z=: 1 2» 



3. Given 2.v*-j-8.';— .20=70 •, to find^. 



First, 2A?*-j-8.vr=:7c-}-20=:90 by transposition^ 

 Then x ^ +n^ ^ 45 ^Y dividing by 2j 

 And .v^-f-4^+4 = 49 by completing the square j 

 Whence .Y-(-2 = \/ ^gzz:']- by extract;ing the root. 

 And consequently x::r 7 — 2=115. .. 



4. Given 3>;* — 3A:-}-6=z5y 5 to find X. 

 Here a;* — Ar-j-,2Z?: i|- by dividing by 3, - 

 And x'' — X=i^ — 2 by transposition ; 



Also A?* — X'\--^=:i^ — 2+^=;j-j by completing the" 

 square. 



And X — -zz^—'n^hj evolution ; 

 Therefore Arnf -f 4=4-. 



5. Given — -J-20y=42-|- ; to find x, 



r^* a: 

 .Here -~ ,----—4:52. _2p|-=22-|- by tcanspositiP-a.; ■- 



» 2^ 

 And ;v' — ~z=44i. by dividing by ~ ; 



2*V ^' 



"Whence ;v*— ~-j^|=44| + ^=441 ^Y -Complet- 

 ing the square. And 



