Final answer:
To complete the square of the equation x² + 7x = 4, you add (7/2)² = 49/4 to both sides, resulting in the new equation x² + 7x + 49/4 = 65/4.
Step-by-step explanation:
To complete the square for the equation x² + 7x = 4, you would add a specific number to both sides of the equation that makes the left side a perfect square trinomial. This number is found by taking half of the coefficient of x, which is 7/2, and then squaring it. Therefore, (7/2)² = 49/4. You add 49/4 to both sides of the equation, resulting in x² + 7x + (49/4) = 4 + (49/4). Simplifying the right side gives a new equation of x² + 7x + (49/4) = (16/4) + (49/4), which is x² + 7x + (49/4) = 65/4.