x^2+1/4x+_?__

To find the missing term in the expression x^2 + (1/4)x + __, we can use the concept of completing the square.

Step 1: Identify the coefficient of x, which is 1/4.
Step 2: Take half of the coefficient and square it. In this case, (1/4)/2 = 1/8, and (1/8)^2 = 1/64.
Step 3: Add the result from step 2 to the expression, x^2 + (1/4)x + __ + 1/64.
Step 4: Rewrite the expression as a perfect square trinomial.
- Group the terms and write them as a square of a binomial, keeping in mind that the coefficient of the middle term is twice the product of the square root of the third term and the square root of the first term.
- In this case, it would be (x + 1/16)^2.
- Therefore, the complete expression is x^2 + (1/4)x + 1/64 = (x + 1/16)^2.

So, the missing term is 1/64.