determine the values of d that complete square of x^2 + dx +49/4
To complete the square of the expression x^2 + dx + 49/4, we need to add (d/2)^2 to make it a perfect square trinomial.
So, the complete square form of the expression is (x + d/2)^2 + 49/4.
Comparing this with the given expression, we can see that (x + d/2)^2 + 49/4 = x^2 + dx + 49/4.
This means that (d/2)^2 = 0, since the variables and constant terms on both sides are the same.
So, (d/2)^2 = 0.
Taking the square root of both sides, we get d/2 = 0.
Multiplying both sides by 2, we get d = 0.
Therefore, the value of d that completes the square is 0.