Final answer:
The value of c for x^2 + 9x + c to be a perfect square trinomial is 20.25, calculated by squaring half the coefficient of x, which is 4.5.
Step-by-step explanation:
The value of c that makes x^2 + 9x + c a perfect square trinomial can be found using the rule for perfect square trinomials. For any quadratic trinomial of the form ax^2 + bx + c to be a perfect square, the constant c must be equal to the square of half the coefficient of x. In this case, the coefficient of x is 9, and half of 9 is 4.5. Squaring 4.5 gives us 20.25, which is the required value of c.
To formulate the perfect square trinomial, we take the expression x^2 + 9x and add the square of half the x-coefficient to it. So, we get x^2 + 9x + (4.5)^2, which simplifies to x^2 + 9x + 20.25. Therefore, c should be 20.25 for the original expression to be a perfect square trinomial.