Find the value of c that makes x^2+26x+c a perfect-square trinomial.

C = 169

square is (x + 13) ^2

Explanation:

In the form:

ax^2 + bx + c

to complete the square a = 1 is required.

c = (b/2) ^2

the square term is b/2

x^2 + 26x + c

a = 1 so we are okay to complete the square.

b = 26

c = (26/2) ^2 = 13^2 = 169

finally to complete the square:

x^2 + 26x + 169 = (x+b/2) ^2 = (x+13) ^2