35? iLLGEBRA. 



4. Extract the square root from both sides of the equa- 

 tion, and the value of the unknown quaxitity wiii be dcr 

 termined, as required. 



Note i. The square root of one side of the equation 

 is always equal to the unknown quantity, with half the co*. 

 efEcient of the second term subjoined to it. 



Note 2. i^ 11 equations, v/herein there are two terms 

 involving the unknown quantity, and the index of one is 

 just double that of the o^iher, are sbived like quadratics 

 by completing the square. 



_«_ 



Thus, x^'-\'^':X^-:zzb, or x'"-\-axrzzl;, are the same as 



quadratics, and the value of the unknov/n quantity may 

 be determined accordingly. 



EXAM^LE$, 



1 /7 



have xzz-^-a/ — — 5 -f- for the affirmative valiic of x, an4 

 43 



• '■* a 



- — y'^ — If 4" — for the negative value of :;, 



But in this third form, if l> be greater than — , the solution of 



4 

 the proposed question will be impossible. For, since the square 

 of any quantity (whether that quantity be affirmative or negative) 

 is always affin-matlve, the square root of a negative quantity is im- 

 possible, and cannot be assigned. But if b be greater than—, 



4 



then — — ii is a aiegative quantity ; and conseauently ^ — — d 

 4 4 



is impossible, or only imaginary, when — is less than b ; and 



-V 



therefore in that case x=z — J^a/ ^ is also impossible or 



24 



imaginary. 



