Quadratic Equations. 57 



Solve the following : 



I. A-^-f 7.^--f-I5 = 5• 

 ^. X- + 6-r — 1 = 5 — 20-V. 



4 . I ^x^— 28-^+10=5. 



In completing the square in a case like this where the coeffi- 

 cient of -T is divisible by 2, fractions can be avoided without 

 multipljdng the equation through by 4. Thus: 



15^^— 28.r= — 5, 

 multiplying through by 15 (instead of 4X15), and adding the 

 square of one-half of 28, w^e obtain 



(i5rx^-i5X28.r+(i4)^=-5Xi5 + (i4)^ 

 which is a complete square. 



5. .t-4-i2yV^'=38t. 



7. jr^H-6.5i = 5.2x. 



P 



8. x^ -\-i—ax— = o. 



q 



10. (x—a)(x—b) = o. 



11. (2^x—^)(sx—2,) = o. 



12. (ax—b)(bx—a)^o. 



I J. (x-^a — d)(x—a-j-d) = o. 

 i^. a^—x^=(a—x)(d-\-c—x). 



15- r33+iO-r/4-r56+io.r;==r65+i4-C- 



16, (^7— 4v/3;A-=-f ,^2— \^3;.v=^. 



18. x^ + qax= d'—b'. 



ig. (x—a)^=(x—b)(a-\-b). 



20. dez'—(d'-^e)z^-de=o. 



21. x^—2a(x-^b) = 2bx—a'—b^. 



22. jt-^-f 10x4-30= 5- 

 2j. a-\-b-\-x=a'b\i\ 



24. -\-ax= , +bx. 

 ^ a b 



25. ax'-\-bx-\-c=x^-\-px-\-q. 



A— 7 



V 



