Final answer:
To complete the square for the equation x² - 7x, the constant term needed is (7/2)² or 49/4, making the left side of the equation a perfect square trinomial.
Step-by-step explanation:
To complete the square for the quadratic equation x² - 7x + ___ = 4, we need to add a constant term that will transform the left side of the equation into a perfect square trinomial. The constant term is found by taking half of the coefficient of the x term, which is -7/2, and then squaring it, resulting in (7/2)² or 49/4. Therefore, the constant term that completes the square is 49/4.
To show the process: x² - 7x + (7/2)² = 4 + (7/2)². When simplified, the left side of the equation becomes (x - 7/2)², which is a perfect square trinomial.