Completing the square: Find the value of c such that each expression is a perfect-square trinomial.
p^2 - 11p + c
Is the answer 30.25? If not, please explain. Thanks
yes
To determine the value of c such that the expression p^2 - 11p + c is a perfect-square trinomial, we need to use the process of completing the square.
Step 1: Take half of the coefficient of the middle term (-11p) and square it:
(-11/2)^2 = 121/4
Step 2: Add the result from step 1 to both sides of the equation:
p^2 - 11p + 121/4 + c = p^2 - 11p + 121/4
Step 3: Factor the perfect-square trinomial on the right side:
(p - 11/2)^2 = p^2 - 11p + 121/4
Step 4: Since we want the given expression to be a perfect-square trinomial, we need c to be equal to 121/4.
Therefore, the correct answer for c is 121/4, which is equivalent to 30.25.
So, yes, your answer of 30.25 is correct.