Final answer:
The value that must be added to the expression x²-3x to make it a perfect-square trinomial is 2.25, which is the square of half the coefficient of x (-1.5).
Step-by-step explanation:
The student asked which value must be added to x²-3x to make it a perfect-square trinomial. To create a perfect-square trinomial from an expression of the form x²+bx, one must add the square of half of the coefficient b of x. In this particular expression, b is -3, so half of -3 is -1.5 and the square of -1.5 is 2.25. Therefore, 2.25 must be added to the expression x²-3x to form a perfect-square trinomial (x - 1.5)², which is x² - 3x + 2.25.
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