Final answer:
To make the expression a perfect square trinomial, set k = 1/4.
Step-by-step explanation:
To make the given expression a perfect square trinomial, we need to find the value of k. The expression is x^2 - (1/4)x + k. We can complete the square by considering the coefficient of x^2, which is 1. We want to make the expression in the form (x - h)^2 + c, where h is half the coefficient of x and c is the constant.
By comparing the given expression with (x - h)^2 + c, we have h = 1/2 and c = k. Therefore, to make it a perfect square trinomial, we set k = (1/2)^2 = 1/4.
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