SOLUTION: Find a value for K that will make 4x^2 + 6.4x + K a perfect square. Describe the procedure used which requires algebra and not trial and error.

Its square root must be a binomial with first term
the square root of  or , and
second term the square root of  or 

So we must have



or



or

 

Add  to both sides:



Divide both sides by 



Square both sides



 

That's the answer, and therefore

 becomes



which equals

, a perfect square.

Edwin