Quandaries
and Queries 

Question: Could you please solve the following for x x^{2}+6=5x 

Hi, I will do a similar problem, x^{2} + 2x = 8 First move all the terms to one side of the equation so that the x^{2} term is positive.
Now I am going to factor the left side. Since the constant term (8) is negative I know that, if I can factor the expression the factorization will have the form
Expanding this I get
Comparing this to x^{2} + 2x  8 I can see that
The problem thus is reduced from factoring an algebraic expression to factoring a number, 8. I want two factors of 8 (a and b) which have a difference of 2. 8 can be factored as 8 = 8 1 but 8  1 = 7.
At this point you should check by expanding the right side of the equation above to verify that it is equal to the right side. Thus the equation
can be rewritten
This implies that either x + 4 = 0 or x  2 = 0. The first gives x = 4 and the second, x = 2. Penny 

