Question

a student was given the equation x^2+6x-13=0 the next step in the students process was x^2+6x+c=13+c state the value of c that creates a perfect square trinomial explain how the value of c is determined

Answer 1

This is the process of completing the square. 
Keep this equation in mind: $ax^2+bx+c$
Basically, to make this a perfect square trinomial, you take half of b and square that value. This will make it so you can compress the left side of the equation into $(x+b)^2 \ or \ (x-b)^2$ depending on the sign in the middle of the original equation.