What is the value of c so thatx squared minus 11 x plus c is a perfect-square trinomial?
To find the value of c so that the trinomial x^2 - 11x + c is a perfect-square trinomial, we want to write it in the form (x - a)^2 for some value of a.
Expanding (x - a)^2 gives us x^2 - 2ax + a^2. Comparing this with x^2 - 11x + c, we see that c = a^2 and -11 = -2a. Solving the second equation for a, we get a = 11/2.
Substituting this value back into c = a^2, we get c = (11/2)^2 = 121/4.
Therefore, the value of c so that x^2 - 11x + c is a perfect-square trinomial is c = 121/4.