determine the values of d that complete square of x^2 + dx +49/4

Answer 1

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.