xsquare + 26x+ c

Question

find the value of c that makes each trinomial a perfect square

Answer 1

Ok, this one isn't too tough.  We don't even have to do a full round of completing the square.  Let's start with what the question is asking.  We want to know what number we can put in for C that will give us an answer of the form:

 

(x + a)^2

 

This general form expands to the form

 

x^2 + 2ax + a^2.

 

We have, from above

 

x^2 + 26x + C.

 

These two equations must be equal, so the coefficient of each variables (x^2, x, or no x) must be the same.  Knowing that, we see that the 26x = 2ax and C = a^2.  We just need to know what a is.  Easy.

 

26x = 2ax     ---     There is an x on each side, so the rest of it that isn't x must be the same:

26 = 2a     ---     Just divide both sides by 2

a = 13.

 

So now we know what a is, and how it relates to the other equation.  We already know that C = a^2.  So C = 13^2.

 

C = 169.